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  • THE BAIRE CATEGORY PROPERTY AND SOME NOTIONS OF COMPACTNESS

  • JULES FOSSY, MARIANNE MORILLON
  • Journal:
    Journal of the London Mathematical Society / Volume 57 / Issue 1 / February 1998
    Published online by Cambridge University Press:
    01 February 1998, pp. 1-19
    Print publication:
    February 1998

  • 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]).