scholarly journals The Baire-category method in some compact extension problems

1986 ◽  
Vol 122 (1) ◽  
pp. 197-210 ◽  
Author(s):  
Elżbieta Pol
Keyword(s):  
Baire Category ◽  
Compact Extension

scholarly journals Stable Analysis of Solution Set for System of Quasivariational Relations with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lefeng Shi ◽  
Zhe Yang
Keyword(s):  
Baire Category ◽  
Solution Set ◽  
Stability Of Solutions ◽  
Essential Component ◽  
Essential Stability ◽  
Essential Components ◽  
Quasivariational Inclusions

The essential stability of solutions for system of quasivariational relations is studied. We show that most of systems of quasivariational relations are essential (in the sense of Baire category) and that, for any system of quasivariational relations, there exists at least one essential component of its solution set. As applications, the existence of essential components of solution set for systems of KKM problems and systems of quasivariational inclusions is obtained.

Density and Baire category in recursive topology

2004 ◽  
Vol 50 (45) ◽  
pp. 381-391
Author(s):  
Iraj Kalantari ◽  
Larry Welch
Keyword(s):  
Baire Category ◽  
Recursive Topology

RESULTS OF BAIRE CATEGORY TYPE IN CONVEXITY

1985 ◽  
Vol 440 (1 Discrete Geom) ◽  
pp. 163-169 ◽  
Author(s):  
Peter M. Gruber
Keyword(s):  
Baire Category ◽  
Category Type

scholarly journals Polish groups and Baire category methods

2016 ◽  
Vol 8 (1) ◽  
pp. 89-164 ◽  
Author(s):  
Julien Melleray
Keyword(s):  
Baire Category ◽  
Polish Groups

scholarly journals On the preservation of Baire and\newline weakly Baire category

2016 ◽  
Vol 141 (4) ◽  
pp. 475-481
Author(s):  
Alireza Kamel Mirmostafaee ◽  
Zbigniew Piotrowski
Keyword(s):  
Baire Category

scholarly journals On pseudocompact topological Brandt λ0-extensions of semitopological monoids

2013 ◽  
Vol 1 ◽  
pp. 60-79
Author(s):  
Oleg Gutik ◽  
Kateryna Pavlyk
Keyword(s):  
Topological Properties ◽  
Countably Compact ◽  
Compact Extension

AbstractIn the paper we investigate topological properties of a topological Brandt λ0-extension B0λ(S) of a semitopological monoid S with zero. In particular we prove that for every Tychonoff pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) semitopological monoid S with zero there exists a unique semiregular pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) extension B0λ(S) of S and establish their Stone-Cˇ ech and Bohr compactifications. We also describe a category whose objects are ingredients in the constructions of pseudocompact (resp., countably compact, sequentially compact, compact) topological Brandt λ0- extensions of pseudocompact (resp., countably compact, sequentially compact, compact) semitopological monoids with zeros.

scholarly journals The closed graph theorem without category

1987 ◽  
Vol 36 (2) ◽  
pp. 283-287 ◽  
Author(s):  
Charles Swartz
Keyword(s):  
Baire Category ◽  
Baire Category Theorem ◽  
Normed Spaces ◽  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph Theorem ◽  
Category Theorem

We show that a diagonal theorem of P. Antosik can be used to give a proof of the Closed Graph Theorem for normed spaces which does not depend upon the Baire Category Theorem.

Γ‎-Null and Γ‎N-Null Sets

2012 ◽  
Author(s):  
Joram Lindenstrauss ◽  
David Preiss ◽  
Tiˇser Jaroslav
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Finite Dimension ◽  
Baire Category ◽  
Borel Sets ◽  
Basic Properties ◽  
Gâteaux Differentiability ◽  
Gateaux Differentiability ◽  
Null Set

This chapter introduces the notions of Γ‎-null and Γ‎ₙ-null sets, which are σ‎-ideals of subsets of a Banach space X. Γ‎-null set is key for the strongest known general Fréchet differentiability results in Banach spaces, whereas Γ‎ₙ-null set presents a new, more refined concept. The reason for these notions comes from an (imprecise) observation that differentiability problems are governed by measure in finite dimension, but by Baire category when it comes to behavior at infinity. The chapter first relates Γ‎-null and Γ‎ₙ-null sets to Gâteaux differentiability before discussing their basic properties. It then describes Γ‎-null and Γ‎ₙ-null sets of low Borel classes and presents equivalent definitions of Γ‎ₙ-null sets. Finally, it considers the separable determination of Γ‎-nullness for Borel sets.

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