Topology and its Applications, ISSN 0166-8641, 2010, Volume 157, Issue 5, pp. 874 - 893

All spaces are assumed to be Tychonoff. A space X is called projectively P (where P is a topological property...

Pseudometric | Strong fan tightness | γ-cover | Cardinal numbers [formula omitted] | Menger space | Property C | [formula omitted]-space | Cozero set | Lindelöf space | formula omitted | wQN-space | Rothberger space | ω-cover | Projectively Rothberger space | [formula omitted]-embedded set | Property ( γ) | AP-space | Projectively Menger space | Strictly Fréchet space | σ-space | Fréchet space | Strong measure zero | Projectively ( γ)-space | Monotonic Sequence Selection Property | Pseudocompact space | Projectively Hurewicz space | Scattered space | Tightness | Reznichenko property | Sequential space | Fan tightness | Property [formula omitted] | Projectively [formula omitted]-space | QN-space | Menger base property | Hurewicz space | The countable fan space | Weakly Fréchet space | Haver property | Weakly Fréchet in the strict sense space | Functionally countable space | Ψ-space | Projectively countable space | Zero set | Zero-dimensional space | Arhangelskii's [formula omitted] properties | space | cov (M) | Projectively (γ)-space | embedded set | Arhangelskii's α | add (M) | X | Projectively ()-space | Property () | Cardinal numbers b | Property (γ) | properties | MATHEMATICS, APPLIED | OPEN COVERS | partial derivative | sigma-space | cov(M) | gamma-cover | Weakly Frechet space | Property (gamma) | FUNCTION-SPACES | Strictly Frechet space | Weakly Frechet in the strict sense space | Arhangelskii's alpha(i) properties | MATHEMATICS | C-p(X) | AP(omega)-space | add(M) | Frechet space | C-embedded set | HUREWICZ | psi-space | Projectively (gamma)-space | Lindelof space | COMBINATORICS | omega-cover

Pseudometric | Strong fan tightness | γ-cover | Cardinal numbers [formula omitted] | Menger space | Property C | [formula omitted]-space | Cozero set | Lindelöf space | formula omitted | wQN-space | Rothberger space | ω-cover | Projectively Rothberger space | [formula omitted]-embedded set | Property ( γ) | AP-space | Projectively Menger space | Strictly Fréchet space | σ-space | Fréchet space | Strong measure zero | Projectively ( γ)-space | Monotonic Sequence Selection Property | Pseudocompact space | Projectively Hurewicz space | Scattered space | Tightness | Reznichenko property | Sequential space | Fan tightness | Property [formula omitted] | Projectively [formula omitted]-space | QN-space | Menger base property | Hurewicz space | The countable fan space | Weakly Fréchet space | Haver property | Weakly Fréchet in the strict sense space | Functionally countable space | Ψ-space | Projectively countable space | Zero set | Zero-dimensional space | Arhangelskii's [formula omitted] properties | space | cov (M) | Projectively (γ)-space | embedded set | Arhangelskii's α | add (M) | X | Projectively ()-space | Property () | Cardinal numbers b | Property (γ) | properties | MATHEMATICS, APPLIED | OPEN COVERS | partial derivative | sigma-space | cov(M) | gamma-cover | Weakly Frechet space | Property (gamma) | FUNCTION-SPACES | Strictly Frechet space | Weakly Frechet in the strict sense space | Arhangelskii's alpha(i) properties | MATHEMATICS | C-p(X) | AP(omega)-space | add(M) | Frechet space | C-embedded set | HUREWICZ | psi-space | Projectively (gamma)-space | Lindelof space | COMBINATORICS | omega-cover

Journal Article

Topology and its Applications, ISSN 0166-8641, 2012, Volume 159, Issue 1, pp. 253 - 271

A space X is called selectively separable ( R-separable) if for every sequence of dense subspaces ( D n : n ∈ ω...

Fréchet space | Radial space | Strong fan tightness | R-separable space | SS + space | D +-separable space | Stratifiable space | Discretely generated space | M-separable space | DH +-separable space | Crowded space | Tightness | Sequential space | GN-separable space | Fan tightness | d-separable space | Resolvable space | Extra-resolvable space | DH-separable space | Separable space | Submaximal space | Whyburn property | H-separable space | Maximal space | D-separable space | TOPOLOGIES | MATHEMATICS, APPLIED | INVARIANTS | RESOLVABILITY | PRINCIPLES | MATHEMATICS | DH+-separable space | Frechet space | D+-separable space | FUNCTION-SPACES | SS+ space | COMPACT

Fréchet space | Radial space | Strong fan tightness | R-separable space | SS + space | D +-separable space | Stratifiable space | Discretely generated space | M-separable space | DH +-separable space | Crowded space | Tightness | Sequential space | GN-separable space | Fan tightness | d-separable space | Resolvable space | Extra-resolvable space | DH-separable space | Separable space | Submaximal space | Whyburn property | H-separable space | Maximal space | D-separable space | TOPOLOGIES | MATHEMATICS, APPLIED | INVARIANTS | RESOLVABILITY | PRINCIPLES | MATHEMATICS | DH+-separable space | Frechet space | D+-separable space | FUNCTION-SPACES | SS+ space | COMPACT

Journal Article

Pattern Recognition, ISSN 0031-3203, 12/2016, Volume 60, pp. 802 - 812

The sample mean is one of the most fundamental concepts in statistics. Properties of the sample mean that are well-defined in Euclidean spaces become unclear in graph spaces...

Majorize–minimize algorithm | Geometric midpoint | Graph edit distance | Fréchet mean | Consistent estimator | Graph matching | Majorize-minimize algorithm | MANIFOLDS | Frechet mean | COMPUTATION | ANALYSIS GEODESIC PCA | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Analysis | Algorithms

Majorize–minimize algorithm | Geometric midpoint | Graph edit distance | Fréchet mean | Consistent estimator | Graph matching | Majorize-minimize algorithm | MANIFOLDS | Frechet mean | COMPUTATION | ANALYSIS GEODESIC PCA | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Analysis | Algorithms

Journal Article

Journal of Fourier Analysis and Applications, ISSN 1069-5869, 2/2017, Volume 23, Issue 1, pp. 141 - 206

We set up a new general coorbit space theory for reproducing representations of a locally compact second countable group G that are not necessarily irreducible nor integrable...

Coorbit spaces | Fréchet spaces | Mathematics | Abstract Harmonic Analysis | Mathematical Methods in Physics | 43A15 | 42B35 | Fourier Analysis | Signal,Image and Speech Processing | 46A04 | Approximations and Expansions | Representations of locally compact groups | 22D10 | Partial Differential Equations | Reproducing formulae | 46F05 | Frechet spaces | MATHEMATICS, APPLIED | INTEGRABLE GROUP-REPRESENTATIONS | FRAMES | ATOMIC DECOMPOSITIONS | BANACH-SPACES | LP-SPACES | SHEARLET TRANSFORM | ADMISSIBLE VECTORS

Coorbit spaces | Fréchet spaces | Mathematics | Abstract Harmonic Analysis | Mathematical Methods in Physics | 43A15 | 42B35 | Fourier Analysis | Signal,Image and Speech Processing | 46A04 | Approximations and Expansions | Representations of locally compact groups | 22D10 | Partial Differential Equations | Reproducing formulae | 46F05 | Frechet spaces | MATHEMATICS, APPLIED | INTEGRABLE GROUP-REPRESENTATIONS | FRAMES | ATOMIC DECOMPOSITIONS | BANACH-SPACES | LP-SPACES | SHEARLET TRANSFORM | ADMISSIBLE VECTORS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2015, Volume 432, Issue 2, pp. 1183 - 1199

We start the systematic study of Fréchet spaces which are ℵ-spaces in the weak topology...

Fréchet space | Weakly ℵ locally convex space | ℵ-space | [formula omitted]-space | Space of continuous functions | ℵ 0 -space | MATHEMATICS | MATHEMATICS, APPLIED | Weakly N locally convex space | N-0-space | Frechet space | N-space

Fréchet space | Weakly ℵ locally convex space | ℵ-space | [formula omitted]-space | Space of continuous functions | ℵ 0 -space | MATHEMATICS | MATHEMATICS, APPLIED | Weakly N locally convex space | N-0-space | Frechet space | N-space

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2013, Volume 403, Issue 1, pp. 13 - 22

Let E be a Fréchet space, i.e. a metrizable and complete locally convex space (lcs), E′′ its strong second dual with a defining sequence of seminorms...

Fréchet space | formula omitted | Countably compact | Web compact spaces | Compact space | Angelicity | C(X) | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | Frechet space | Sects

Fréchet space | formula omitted | Countably compact | Web compact spaces | Compact space | Angelicity | C(X) | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | Frechet space | Sects

Journal Article

7.
Full Text
Topological properties of strict (LF)-spaces and strong duals of Montel strict (LF)-spaces

Monatshefte für Mathematik, ISSN 0026-9255, 5/2019, Volume 189, Issue 1, pp. 91 - 99

Following Banakh and Gabriyelyan (Monatshefte Math 180:39–64, 2016), a Tychonoff space X is Ascoli if every compact subset of $$C_k(X)$$ C k ( X ) is equicontinuous...

Montel space | Fréchet–Urysohn space | Strict ( LF )-space | 46A13 | Mathematics, general | 46A11 | Mathematics | Ascoli property | Sequential space | 22A05 | Strict (LF)-space | MATHEMATICS | Frechet-Urysohn space

Montel space | Fréchet–Urysohn space | Strict ( LF )-space | 46A13 | Mathematics, general | 46A11 | Mathematics | Ascoli property | Sequential space | 22A05 | Strict (LF)-space | MATHEMATICS | Frechet-Urysohn space

Journal Article

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, ISSN 0036-1410, 2019, Volume 51, Issue 3, pp. 2261 - 2285

In this paper, a regularization of Wasserstein barycenters for random measures supported on R-d is introduced via convex penalization. The existence and...

MATHEMATICS, APPLIED | convex penalization | Bregman divergence | Wasserstein space | regularization | barycenter of probability measures | CONVERGENCE | Frechet mean | Signal and Image Processing | Statistics | Statistics Theory | Computer Science

MATHEMATICS, APPLIED | convex penalization | Bregman divergence | Wasserstein space | regularization | barycenter of probability measures | CONVERGENCE | Frechet mean | Signal and Image Processing | Statistics | Statistics Theory | Computer Science

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 03/2017, Volume 272, Issue 5, pp. 1876 - 1891

The Gurariĭ space is the unique separable Banach space G which is of almost universal disposition for finite-dimensional Banach spaces, which means that for every ε...

The Gurariĭ space | Universality | Graded Fréchet space | SPLITTING THEOREM | MATHEMATICS | Graded Frechet space | BANACH-SPACES | The Gurarli space

The Gurariĭ space | Universality | Graded Fréchet space | SPLITTING THEOREM | MATHEMATICS | Graded Frechet space | BANACH-SPACES | The Gurarli space

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2016, Volume 441, Issue 2, pp. 744 - 762

Let P2,ac be the set of Borel probabilities on Rd with finite second moment and absolutely continuous with respect to Lebesgue measure. We consider the problem...

Location-scatter families | Fixed-point iteration | Wasserstein barycenter | Mass transportation problem | Fréchet mean | [formula omitted]-Wasserstein distance | Wasserstein distance | L | REARRANGEMENT | MATHEMATICS | MATHEMATICS, APPLIED | L-2-Wasserstein distance | Frechet mean | UNIQUENESS | Numerical analysis

Location-scatter families | Fixed-point iteration | Wasserstein barycenter | Mass transportation problem | Fréchet mean | [formula omitted]-Wasserstein distance | Wasserstein distance | L | REARRANGEMENT | MATHEMATICS | MATHEMATICS, APPLIED | L-2-Wasserstein distance | Frechet mean | UNIQUENESS | Numerical analysis

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2019, Volume 478, Issue 2, pp. 1085 - 1099

A fundamental result proved by Bourgain, Fremlin and Talagrand states that the space B1(M...

Baire functions | Ascoli | Normal space | κ-Fréchet–Urysohn | k-Space | MATHEMATICS | MATHEMATICS, APPLIED | kappa-Frechet-Urysohn | ASCOLI PROPERTY | COMPACT SUBSETS

Baire functions | Ascoli | Normal space | κ-Fréchet–Urysohn | k-Space | MATHEMATICS | MATHEMATICS, APPLIED | kappa-Frechet-Urysohn | ASCOLI PROPERTY | COMPACT SUBSETS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2015, Volume 432, Issue 2, pp. 954 - 964

We show that all positive functionals as well as all derivations of the non-commutative Schwartz space are continuous...

Fréchet space | Derivation | Positive functional | Bimodule | Amenable algebra | (Fréchet) lmc-algebra | MATHEMATICS, APPLIED | FRECHET ALGEBRAS | BANACH-ALGEBRAS | DERIVATIONS | MATHEMATICS | APPROXIMATE | (Frechet) lmc-algebra | Frechet space | GENERALIZED NOTIONS | FUNCTIONALS | Algebra

Fréchet space | Derivation | Positive functional | Bimodule | Amenable algebra | (Fréchet) lmc-algebra | MATHEMATICS, APPLIED | FRECHET ALGEBRAS | BANACH-ALGEBRAS | DERIVATIONS | MATHEMATICS | APPROXIMATE | (Frechet) lmc-algebra | Frechet space | GENERALIZED NOTIONS | FUNCTIONALS | Algebra

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2017, Volume 452, Issue 1, pp. 646 - 658

For a compact space K we denote by Cw(K) (Cp(K)) the space of continuous real-valued functions on K endowed with the weak (pointwise) topology...

Weak topology | [formula omitted] space | Fréchet–Urysohn space | Sequential space | Function space | Pointwise convergence topology | (X) space | MATHEMATICS | MATHEMATICS, APPLIED | C-p (X) space | T-EQUIVALENCE | Frechet-Urysohn space

Weak topology | [formula omitted] space | Fréchet–Urysohn space | Sequential space | Function space | Pointwise convergence topology | (X) space | MATHEMATICS | MATHEMATICS, APPLIED | C-p (X) space | T-EQUIVALENCE | Frechet-Urysohn space

Journal Article

2016, London Mathematical Society lecture note series, ISBN 1316601951, Volume 428., xii, 302

Many geometrical features of manifolds and fibre bundles modelled on Fréchet spaces either cannot be defined or are difficult to handle directly...

Fréchet spaces | Geometry, Differential | Banach spaces | Fraechet spaces | Frechet spaces

Fréchet spaces | Geometry, Differential | Banach spaces | Fraechet spaces | Frechet spaces

Book

Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2007, Volume 135, Issue 8, pp. 2505 - 2518

We extend some fixed point theorems in L-spaces, obtaining extensions of the Banach fixed point theorem to partially ordered sets.

Mathematical sequences | Frechet topologies | Mathematical theorems | Mathematical monotonicity | Topological theorems | Abstract spaces | Diagonal lemma | Partially ordered sets | Mathematics | Topological spaces | L-spaces | Partially ordered set | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | partially ordered set | fixed point | SETS | EQUATIONS

Mathematical sequences | Frechet topologies | Mathematical theorems | Mathematical monotonicity | Topological theorems | Abstract spaces | Diagonal lemma | Partially ordered sets | Mathematics | Topological spaces | L-spaces | Partially ordered set | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | partially ordered set | fixed point | SETS | EQUATIONS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 12/2018, Volume 339, pp. 495 - 539

A Fréchet space X satisfies the Hereditary Invariant Subspace (resp. Subset) Property if for every closed infinite-dimensional subspace M in X, each continuous operator on M possesses a non-trivial invariant subspace (resp. subset...

Invariant subspaces | Fréchet spaces | Invariant subsets | Frechet spaces | MATHEMATICS | BANACH-SPACES | CLOSED SUBSPACES | OPERATORS

Invariant subspaces | Fréchet spaces | Invariant subsets | Frechet spaces | MATHEMATICS | BANACH-SPACES | CLOSED SUBSPACES | OPERATORS

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 2019, Volume 346, pp. 84 - 109

.... We develop gradient descent algorithm based on Fréchet differentiability in Hilbert–Besov spaces complemented...

Calibration of parameters | Inverse Stefan problem | Optimal control of parabolic free boundary problem | Tikhonov regularization | Gradient method in Hilbert–Besov spaces | Fréchet gradient preconditioning | MATHEMATICS, APPLIED | Frechet gradient preconditioning | OPTIMAL RECONSTRUCTION | Gradient method in Hilbert Besov spaces | CAUCHY-PROBLEM | CONVERGENCE | REGULARIZATION | FRECHET DIFFERENTIABILITY | Analysis | Methods | Algorithms

Calibration of parameters | Inverse Stefan problem | Optimal control of parabolic free boundary problem | Tikhonov regularization | Gradient method in Hilbert–Besov spaces | Fréchet gradient preconditioning | MATHEMATICS, APPLIED | Frechet gradient preconditioning | OPTIMAL RECONSTRUCTION | Gradient method in Hilbert Besov spaces | CAUCHY-PROBLEM | CONVERGENCE | REGULARIZATION | FRECHET DIFFERENTIABILITY | Analysis | Methods | Algorithms

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 9/2019, Volume 42, Issue 5, pp. 2535 - 2547

... -space in paratopological loops are discussed, which improves some known conclusions. Finally, a few questions about paratopological loops are posed.

54A20 | 54E99 | 54D55 | 54D99 | aleph $$ ℵ -spaces | Sequential spaces | Mathematics | 54H99 | Strongly Fréchet–Urysohn spaces | 54E35 | Fréchet–Urysohn spaces | Mathematics, general | Applications of Mathematics | Metrizable spaces | Paratopological loops | MATHEMATICS | N-spaces | GYROGROUPS | SPACES | Frechet-Urysohn spaces | Strongly Frechet-Urysohn spaces | Group theory

54A20 | 54E99 | 54D55 | 54D99 | aleph $$ ℵ -spaces | Sequential spaces | Mathematics | 54H99 | Strongly Fréchet–Urysohn spaces | 54E35 | Fréchet–Urysohn spaces | Mathematics, general | Applications of Mathematics | Metrizable spaces | Paratopological loops | MATHEMATICS | N-spaces | GYROGROUPS | SPACES | Frechet-Urysohn spaces | Strongly Frechet-Urysohn spaces | Group theory

Journal Article

STATISTICAL SCIENCE, ISSN 0883-4237, 05/2019, Volume 34, Issue 2, pp. 236 - 252

.... Regression methods on this shape space are not trivial because this space has a complex finite-dimensional Riemannian manifold structure (non-Euclidean...

Shape space | Kernel regression | METRICS | PATHS | STATISTICS & PROBABILITY | statistical shape analysis | Frechet mean | children's wear | NEWTONS METHOD | SETS | PLANAR SHAPES | CONVERGENCE | RIEMANNIAN-MANIFOLDS

Shape space | Kernel regression | METRICS | PATHS | STATISTICS & PROBABILITY | statistical shape analysis | Frechet mean | children's wear | NEWTONS METHOD | SETS | PLANAR SHAPES | CONVERGENCE | RIEMANNIAN-MANIFOLDS

Journal Article

Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 02/2017, Volume 53, Issue 1, pp. 1 - 26

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space of probability measures on the line, with finite second moment, endowed with the Wasserstein metric...

Geodesic space | Geodesic and Convex Principal Component Analysis | Inference for family of densities | Fréchet mean | Functional data analysis | Wasserstein space | SHAPE | PRINCIPAL COMPONENT ANALYSIS | STATISTICS & PROBABILITY | FUNCTIONAL PRINCIPAL | MANIFOLDS | Frechet mean | INFERENCE | Probability | Statistics | Mathematics

Geodesic space | Geodesic and Convex Principal Component Analysis | Inference for family of densities | Fréchet mean | Functional data analysis | Wasserstein space | SHAPE | PRINCIPAL COMPONENT ANALYSIS | STATISTICS & PROBABILITY | FUNCTIONAL PRINCIPAL | MANIFOLDS | Frechet mean | INFERENCE | Probability | Statistics | Mathematics

Journal Article