scholarly journals A dichotomy theorem for the generalized Baire space and elementary embeddability at uncountable cardinals

2017 ◽  
Vol 238 (1) ◽  
pp. 53-78
Author(s):  
Dorottya Sziráki ◽  
Jouko Väänänen
Keyword(s):  
Baire Space ◽  
Dichotomy Theorem ◽  
Uncountable Cardinals

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.

NEGATIVE PARTITION RELATIONS OR UNCOUNTABLE CARDINALS OF COFINALITY

2001 ◽  
Vol 37 (1-2) ◽  
pp. 233-236
Author(s):  
P. Matet
Keyword(s):  
Partition Relations ◽  
Uncountable Cardinals

We modify an argument of Baumgartner to show that…

scholarly journals Freely indecomposable almost free groups with free abelianization

2020 ◽  
Vol 23 (3) ◽  
pp. 531-543
Author(s):  
Samuel M. Corson
Keyword(s):  
Free Groups ◽  
Uncountable Cardinals

AbstractFor certain uncountable cardinals κ, we produce a group of cardinality κ which is freely indecomposable, strongly κ-free, and whose abelianization is free abelian of rank κ. The construction takes place in Gödel’s constructible universe L. This strengthens an earlier result of Eklof and Mekler.

The weak König lemma and uniform continuity

2008 ◽  
Vol 73 (3) ◽  
pp. 933-939 ◽  
Author(s):  
Josef Berger
Keyword(s):  
Continuous Function ◽  
Uniform Continuity ◽  
Baire Space ◽  
Cantor Space

AbstractWe prove constructively that the weak König lemma and quantifier-free number–number choice imply that every pointwise continuous function from Cantor space into Baire space has a modulus of uniform continuity.

scholarly journals Baire space and second category extensions

1981 ◽  
Vol 12 (2) ◽  
pp. 135-140 ◽  
Author(s):  
John W. Carlson
Keyword(s):  
Baire Space ◽  
Second Category
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