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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
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
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 2/2017, Volume 23, Issue 1, pp. 141 - 206
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2015, Volume 432, Issue 2, pp. 1183 - 1199
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
Journal Article
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
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
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
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
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
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
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
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
Book
Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2007, Volume 135, Issue 8, pp. 2505 - 2518
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
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
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
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
Journal Article