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Products of compact spaces and the axiom of choice II

โœ Scribed by Omar De la Cruz; Eric Hall; Paul Howard; Kyriakos Keremedis; Jean E. Rubin

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
271 KB
Volume
49
Category
Article
ISSN
0044-3050

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โœฆ Synopsis

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 that the multiple choice axiom has on such products.

๐Ÿ“œ SIMILAR VOLUMES

Products of Compact Spaces and the Axiom
Products of Compact Spaces and the Axiom of Choice
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
Metric spaces and the axiom of choice
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.

The Compactness of 2โ„ and the Axiom of C
The Compactness of 2โ„ and the Axiom of Choice
โœ Kyriakos Keremedis ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 103 KB ๐Ÿ‘ 1 views

We show that for every well ordered cardinal number m the Tychonoff product 2 m is a compact space without the use of any choice but in Cohen's Second Model 2 R is not compact.