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Filters, Antichains and Towers in Topological Spaces and the Axiom of Choice

โœ Scribed by Kyriakos Keremedis


Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
463 KB
Volume
44
Category
Article
ISSN
0044-3050

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โœฆ Synopsis


We find some characterizations of the Axiom of Choice (AC) in terms of certain families of open sets in TI spaces.


๐Ÿ“œ SIMILAR VOLUMES


Metric spaces and the axiom of choice
โœ Omar De la Cruz; Eric Hall; Paul Howard; Kyriakos Keremedis; Jean E. Rubin ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 173 KB ๐Ÿ‘ 1 views

## Abstract We study conditions for a topological space to be metrizable, properties of metrizable spaces, and the role the axiom of choice plays in these matters.

Products of Compact Spaces and the Axiom
โœ Omar De la Cruz; Eric Hall; Paul Howard; Kyriakos Keremedis; Jean E. Rubin ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 156 KB ๐Ÿ‘ 1 views
TWO TOPOLOGICAL EQUIVALENTS OF THE AXIOM
โœ Eric Schechter; E. Schechter ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 159 KB ๐Ÿ‘ 1 views

## Abstract We show that the Axiom of Choice is equivalent to each of the following statements: (i) A product of closures of subsets of topological spaces is equal to the closure of their product (in the product topology); (ii) A product of complete uniform spaces is complete.

Products of compact spaces and the axiom
โœ Omar De la Cruz; Eric Hall; Paul Howard; Kyriakos Keremedis; Jean E. Rubin ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 271 KB

## Abstract This is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces (first and second countable spaces, Hausdorff spaces, and subspaces of โ„^__K__^). We also study well ordered Tychonoff products and the effect