Algebra, Logic and Topology

 

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Author(s)
Gonçalo Gutierres;

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

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 other.

Journal
Mathematical Logic Quarterly

Volume
49

Year
2003

Issue
3

Page(s)
293-298

 
     
 

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