The Baire Category Property and Some Notions of Compactness | Zendy

Fossy Jules | Zendy; Morillon Marianne | Zendy

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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 ]).

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