Constructing Moore spaces with the Baire property from dense metric subspaces

2021 ◽  
pp. 107902
Author(s):  
Vivienne Faurot ◽  
David L. Fearnley
Keyword(s):  
Baire Property ◽  
Moore Spaces

scholarly journals ON DENSE EMBEDDINGS INTO MOORE SPACES WITH THE BAIRE PROPERTY

2010 ◽  
Vol 83 (1) ◽  
pp. 1-10
Author(s):  
DAVID L. FEARNLEY ◽  
LAWRENCE FEARNLEY
Keyword(s):  
Baire Property ◽  
Moore Space ◽  
Moore Spaces

AbstractWe demonstrate a construction that will densely embed a Moore space into a Moore space with the Baire property when this is possible. We also show how this technique generates a new ‘if and only if’ condition for determining when Moore spaces can be densely embedded in Moore spaces with the Baire property, and briefly discuss how this condition can can be used to generate new proofs that certain Moore spaces cannot be densely embedded in Moore spaces with the 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.

Joint continuity of K h C-functions with values in moore spaces

2008 ◽  
Vol 60 (11) ◽  
pp. 1803-1812 ◽  
Author(s):  
V. K. Maslyuchenko ◽  
V. V. Mykhailyuk ◽  
O. I. Filipchuk
Keyword(s):  
Joint Continuity ◽  
Moore Spaces
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