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Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2016, Volume 434, Issue 1, pp. 182 - 190
In this paper, author proves that if X1 and X2 are Gâteaux differentiable space, then X1 and X2 have the ball-covering property if and only if (X1×X2,‖⋅‖p) and (X1×X2... 
Gâteaux differentiable space | Ball-covering property | Convex function | MATHEMATICS | MATHEMATICS, APPLIED | MAPPINGS | WEAK ASPLUND SPACES | Gateaux differentiable space | CONVEX-FUNCTIONS | FRECHET DIFFERENTIABILITY | Bisphenol-A
Journal Article
Topology and its Applications, ISSN 0166-8641, 2012, Volume 159, Issue 1, pp. 183 - 193
Let ( X , τ ) be a topological space and let ρ be a metric defined on X. We shall say that ( X , τ ) is fragmented by ρ if whenever ε > 0 and A is a nonempty subset of X there is a... 
Fragmentable | σ-Fragmentable | Function spaces | Topological groups | MATHEMATICS, APPLIED | NORMS | WEAK ASPLUND | MATHEMATICS | CONTINUITY | SIGMA-FRAGMENTABILITY | CONTINUOUS-MAPPINGS | sigma-Fragmentable | BANACH-SPACES | RADON-NIKODYM PROPERTY | SETS | OPTIMIZATION | ASPLUND SPACES
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2006, Volume 134, Issue 9, pp. 2745 - 2754
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2003, Volume 131, Issue 2, pp. 647 - 654
Journal Article
by Raja, M
Journal of Functional Analysis, ISSN 0022-1236, 2003, Volume 197, Issue 1, pp. 1 - 13
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2013, Volume 405, Issue 1, pp. 297 - 309
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 04/2015, Volume 91, Issue 2, pp. 303 - 310
In a recent paper, topological spaces $(X,{\it\tau})$ that are fragmented by a metric that generates the discrete topology were investigated... 
Fragmentable | Sigma-scattered | Topological game | WEAK ASPLUND SPACE | MATHEMATICS | sigma-scattered | CONTINUITY | SIGMA-FRAGMENTABILITY | CONTINUOUS-MAPPINGS | BANACH-SPACES | RADON-NIKODYM PROPERTY | NORM | OPTIMIZATION | DIFFERENTIATION | fragmentable | topological game
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2001, Volume 129, Issue 12, pp. 3741 - 3747
Under the assumption that there exists in the unit interval [0,1] an uncountable set A with the property that every continuous mapping from a Baire metric space... 
Unit ball | Topological theorems | Homeomorphism | Mathematical functions | Topology | Banach space | Topological spaces | Continuous functions | Weak asplund space | Baire space | Double arrow space | Stegall's class | Minimal usco | Fragmentability | fragmentability | MATHEMATICS | MATHEMATICS, APPLIED | weak Asplund space | double arrow space | minimal usco
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2005, Volume 133, Issue 2, pp. 425 - 429
Assuming the consistency of the existence of a measurable cardinal, it is consistent to have two Banach spaces, X,Y, where X is a weak Asplund space such that X^{*} (in the weak* topology... 
Mathematical set theory | Mathematical theorems | Kalinda | Axioms | Mathematical analysis | Mathematical functions | Banach space | Topological spaces | Weak Asplund space | Fragmentable space | Measurable cardinal | Stegall's class of spaces | MATHEMATICS | measurable cardinal | MATHEMATICS, APPLIED | weak Asplund space | COHEN EXTENSIONS | fragmentable space | PRECIPITOUS IDEALS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/2002, Volume 130, Issue 7, pp. 2139 - 2143
We show that, under some additional set-theoretical assumptions which are equiconsistent with the existence of a measurable cardinal, there is a weak Asplund space whose dual, equipped with the weak... 
Mathematical theorems | Kalinda | Martins axiom | Mathematics | Mathematical functions | Local extrema | Banach space | Continuum hypothesis | Topological spaces | Continuous functions | Weak Asplund space | Fragmentable space | Stegall's class of spaces | MATHEMATICS | MATHEMATICS, APPLIED | weak Asplund space | fragmentable space
Journal Article
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, ISSN 1345-4773, 2017, Volume 18, Issue 10, pp. 1867 - 1882
In this paper, some necessary and sufficient conditions for Gateaux differentiability of w*-lower semicontinuous convex function of X** are given. Moreover, we... 
MATHEMATICS | MATHEMATICS, APPLIED | Asplund space | ball-covering property | WEAK ASPLUND | convex function | FRECHET DIFFERENTIABILITY | Gateaux differentiability
Journal Article
STUDIA MATHEMATICA, ISSN 0039-3223, 2008, Volume 184, Issue 3, pp. 249 - 262
We consider the class of compact spaces K-A which are modifications of the well known double arrow space... 
MATHEMATICS | BAIRE CLASS FUNCTIONS | COMPACT SPACES | CLASSIFICATION | WEAK ASPLUND SPACE | SETS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 10/1987, Volume 303, Issue 2, pp. 517 - 527
We show that, typically, lower semicontinuous functions on a Banach space densely inherit lower subderivatives of the same degree of smoothness as the norm... 
Mathematical theorems | Nonsmooth analysis | Hilbert spaces | Mathematical functions | Mathematical inequalities | Banach space | Distance functions | Ekeland’s principle | Proximal normals | Weak Asplund spaces | Renorms | Sub derivatives
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 4/1992, Volume 114, Issue 4, pp. 1003 - 1008
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 7/1988, Volume 103, Issue 3, pp. 773 - 778
...)$ of nonsupport points of a closed convex subset $C$ of a Banach space $E$, which is assumed to be either an Asplund space... 
Hausdorff spaces | Rain | Mathematical theorems | Maps | Mathematical functions | Banach space | Topological spaces | Weak Asplund spaces | Convex sets | Asplund spaces | Convex functions | Support points | Usco maps
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 9/1990, Volume 110, Issue 1, pp. 117 - 123
Subdifferentials of convex functions and some regular functions f are expressed in terms of limiting gradients at points in a given dense subset of . 
Banach space | Directional derivatives | Mathematical functions | Directionally Lipschitz functions | Weak Asplund spaces | Pseudoregular functions | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Set-Valued Analysis, ISSN 0927-6947, 12/2001, Volume 9, Issue 4, pp. 383 - 390
... (2000): 28A35, 46E15, 46E47, 46N10, 47H05, 90C48. Key words: general Monge–Kantorovich problem, Borel measure, support function, subdifferential, space... 
Geometry | subdifferential | weak Asplund space | support function | Analysis | Mathematics | Borel measure | space of continuous functions | general Monge-Kantorovich problem | Weak Asplund space | Support function | General Monge-Kantorovich problem | Subdifferential | Space of continuous functions | MATHEMATICS, APPLIED
Journal Article
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