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 Polish groups admitting non-essentially countable actions

2020 ◽  
pp. 1-15
Author(s):  
ALEXANDER S. KECHRIS ◽  
MACIEJ MALICKI ◽  
ARISTOTELIS PANAGIOTOPOULOS ◽  
JOSEPH ZIELINSKI
Keyword(s):  
Equivalence Relation ◽  
Isometry Group ◽  
Alternative Proof ◽  
Orbit Equivalence ◽  
Locally Compact ◽  
Continuous Action ◽  
Polish Groups ◽  
Infinite Dimensional ◽  
Open Question ◽  
New Criterion

Abstract It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. We answer this question positively for the class of all Polish groups that embed in the isometry group of a locally compact metric space. This class contains all non-archimedean Polish groups, for which we provide an alternative proof based on a new criterion for non-essential countability. Finally, we provide the following variant of a theorem of Solecki: every infinite-dimensional Banach space has a continuous action whose orbit equivalence relation is Borel but not essentially countable.

scholarly journals Homogeneous spaces and transitive actions by Polish groups

2008 ◽  
Vol 165 (1) ◽  
pp. 133-159 ◽  
Author(s):  
Jan van Mill
Keyword(s):  
Homogeneous Spaces ◽  
Polish Groups ◽  
Transitive Actions

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

scholarly journals AUTOMORPHISM GROUPS OF RANDOMIZED STRUCTURES

2017 ◽  
Vol 82 (3) ◽  
pp. 1150-1179 ◽  
Author(s):  
TOMÁS IBARLUCÍA
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Original Structure ◽  
Polish Groups ◽  
Separable Models

AbstractWe study automorphism groups of randomizations of separable structures, with focus on the ℵ0-categorical case. We give a description of the automorphism group of the Borel randomization in terms of the group of the original structure. In the ℵ0-categorical context, this provides a new source of Roelcke precompact Polish groups, and we describe the associated Roelcke compactifications. This allows us also to recover and generalize preservation results of stable and NIP formulas previously established in the literature, via a Banach-theoretic translation. Finally, we study and classify the separable models of the theory of beautiful pairs of randomizations, showing in particular that this theory is never ℵ0-categorical (except in basic cases).

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 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

A Baire category approach in existence theory of differential equations

1998 ◽  
Vol 68 (1) ◽  
pp. 145-151
Author(s):  
Giulio Pianigiani
Keyword(s):  
Differential Equations ◽  
Baire Category ◽  
Existence Theory

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.

Sign in / Sign up

Export Citation Format

Share Document