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Sequential topological conditions in ℝ in the absence of the axiom of choice

✍ Scribed by Gonçalo Gutierres

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

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✦ Synopsis

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 of the axiom of choice, and that they are equivalent to each

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