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TWO TOPOLOGICAL EQUIVALENTS OF THE AXIOM OF CHOICE

✍ Scribed by Eric Schechter; E. Schechter

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
159 KB
Volume
38
Category
Article
ISSN
0044-3050

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✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

Sequential topological conditions in ℝ i
Sequential topological conditions in ℝ in the absence of the axiom of choice
✍ GonΓ§alo Gutierres πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 115 KB

## Abstract It is known that – assuming the axiom of choice – for subsets __A__ of ℝ the following hold: (a) __A__ is compact iff it is sequentially compact, (b) __A__ is complete iff it is closed in ℝ, (c) ℝ is a sequential space. We will show that these assertions are not provable in the absence