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Tychonoff products of super second countable and super separable metric spaces

Horst Herrlich, Kyriakos Keremedis, Eleftherios Tachtsis (2008)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Tychonoff Products of Two-Element Sets and Some Weakenings of the Boolean Prime Ideal Theorem

Kyriakos Keremedis (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

Let X be an infinite set, and (X) the Boolean algebra of subsets of X. We consider the following statements: BPI(X): Every proper filter of (X) can be extended to an ultrafilter. UF(X): (X) has a free ultrafilter. We will show in ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) that the following four statements are equivalent: (i) BPI(ω). (ii) The Tychonoff product $2^{ℝ}$ , where 2 is the discrete space 0,1, is compact. (iii) The Tychonoff product ${[0, 1]}^{ℝ}$ is compact. (iv) In a Boolean algebra...

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Tychonoff products of super second countable and super separable metric spaces

Tychonoff Products of Two-Element Sets and Some Weakenings of the Boolean Prime Ideal Theorem

Currently displaying 21 – 22 of 22