scholarly journals Extending Baire Property by countably many sets

2000 ◽  
Vol 129 (1) ◽  
pp. 271-278 ◽  
Author(s):  
Piotr Zakrzewski
Keyword(s):  
Baire Property

scholarly journals CONTINUITY OF MEASURABLE HOMOMORPHISMS

2008 ◽  
Vol 78 (1) ◽  
pp. 171-176 ◽  
Author(s):  
JANUSZ BRZDȨK
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Baire Property ◽  
Topological Groups ◽  
Locally Compact ◽  
Compact Topological Group ◽  
Locally Compact Topological Group

AbstractWe give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.

On Lower and Semi-Lower Density Operators

2007 ◽  
Vol 14 (4) ◽  
pp. 661-671
Author(s):  
Jacek Hejduk ◽  
Anna Loranty
Keyword(s):  
Density Operator ◽  
Baire Property ◽  
Density Operators ◽  
Dense Sets ◽  
Meager Sets ◽  
Algebras Of Sets

Abstract This paper contains some results connected with topologies generated by lower and semi-lower density operators. We show that in some measurable spaces (𝑋, 𝑆, 𝐽) there exists a semi-lower density operator which does not generate a topology. We investigate some properties of nowhere dense sets, meager sets and σ-algebras of sets having the Baire property, associated with the topology generated by a semi-lower density operator.

scholarly journals Baire property and axiom of choice

1993 ◽  
Vol 84 (3) ◽  
pp. 435-450 ◽  
Author(s):  
Haim Judah ◽  
Saharon Shelah
Keyword(s):  
Axiom Of Choice ◽  
Baire Property

TOPOLOGIES RELATED TO SETS HAVING THE BAIRE PROPERTY

1989 ◽  
Vol 22 (1) ◽  
Author(s):  
Ewa Łazarow ◽  
Roy A. Johnson ◽  
Wladyslaw Wilczynski
Keyword(s):  
Baire Property

The Baire property on the hyperspace of nontrivial convergent sequences

2020 ◽  
pp. 107505
Author(s):  
S. García-Ferreira ◽  
R. Rojas-Hernández ◽  
Y.F. Ortiz-Castillo
Keyword(s):  
Baire Property ◽  
Convergent Sequences

scholarly journals Note on limits of simply continuous and cliquish functions

1994 ◽  
Vol 17 (3) ◽  
pp. 447-450 ◽  
Author(s):  
Janina Ewert
Keyword(s):  
Metric Space ◽  
Continuous Functions ◽  
Baire Space ◽  
Baire Property ◽  
Baire Class ◽  
Class 1 ◽  
Pointwise Limit ◽  
Separable Metric Space

The main result of this paper is that any functionfdefined on a perfect Baire space(X,T)with values in a separable metric spaceYis cliquish (has the Baire property) iff it is a uniform (pointwise) limit of sequence{fn:n≥1}of simply continuous functions. This result is obtained by a change of a topology onXand showing that a functionf:(X,T)→Yis cliquish (has the Baire property) iff it is of the Baire class 1 (class 2) with respect to the new topology.

THE BAIRE PROPERTY IN THE REMAINDERS OF SEMITOPOLOGICAL GROUPS

2013 ◽  
Vol 88 (2) ◽  
pp. 301-308 ◽  
Author(s):  
LI-HONG XIE ◽  
SHOU LIN
Keyword(s):  
Positive Answer ◽  
Baire Space ◽  
Baire Property ◽  
Topological Groups ◽  
Dichotomy Theorem ◽  
Semitopological Group

AbstractIt is proved that every remainder of a nonlocally compact semitopological group $G$ is a Baire space if and only if $G$ is not Čech-complete, which improves a dichotomy theorem of topological groups by Arhangel’skiǐ [‘The Baire property in remainders of topological groups and other results’, Comment. Math. Univ. Carolin. 50(2) (2009), 273–279], and also gives a positive answer to a question of Lin and Lin [‘About remainders in compactifications of paratopological groups’, ArXiv: 1106.3836v1 [Math. GN] 20 June 2011]. We also show that for a nonlocally compact rectifiable space $G$ every remainder of $G$ is either Baire, or meagre and Lindelöf.

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