Premium
The Baire Category Property and Some Notions of Compactness
Author(s) -
Fossy Jules,
Morillon Marianne
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798005675
Subject(s) - mathematics , hausdorff space , axiom of choice , baire category theorem , baire space , baire measure , axiom , urysohn and completely hausdorff spaces , compact space , nowhere dense set , regular polygon , pure mathematics , discrete mathematics , complete metric space , set theory , set (abstract data type) , metric space , hausdorff measure , hausdorff dimension , computer science , geometry , programming language
We work in set theory without the axiom of choice: ZF . We show that the axiom BC : Compact Hausdorff spaces are Baire , is equivalent to the following axiom: Every tree has a subtree whose levels are finite , which was introduced by Blass (cf. [ 4 ]). This settles a question raised by Brunner (cf. [ 9 , p. 438]). We also show that the axiom of Dependent Choices is equivalent to the axiom: In a Hausdorff locally convex topological vector space, convex‐compact convex sets are Baire . Here convex‐compact is the notion which was introduced by Luxemburg (cf. [ 16 ]).