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Fall 1999 Nonconstructive Properties of Well-Ordered T2 topological Spaces
Kyriakos Keremedis, Eleftherios Tachtsis
Notre Dame J. Formal Logic 40(4): 548-553 (Fall 1999). DOI: 10.1305/ndjfl/1012429718

Abstract

We show that none of the following statements is provable in Zermelo-Fraenkel set theory (ZF) answering the corresponding open questions from Brunner in ``The axiom of choice in topology'':

(i) For every T2 topological space (X, T) if X is well-ordered, then X has a well-ordered base,

(ii) For every T2 topological space (X, T), if X is well-ordered, then there exists a function f : X × W $ \rightarrow$ T such that W is a well-ordered set and f ({x} × W) is a neighborhood base at x for each x $ \in$ X,

(iii) For every T2 topological space (X, T), if X has a well-ordered dense subset, then there exists a function f : X × W $ \rightarrow$ T such that W is a well-ordered set and {x} = $ \cap$ f ({x} × W) for each x $ \in$ X.

Citation

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Kyriakos Keremedis. Eleftherios Tachtsis. "Nonconstructive Properties of Well-Ordered T2 topological Spaces." Notre Dame J. Formal Logic 40 (4) 548 - 553, Fall 1999. https://doi.org/10.1305/ndjfl/1012429718

Information

Published: Fall 1999
First available in Project Euclid: 30 January 2002

zbMATH: 0988.54006
MathSciNet: MR1858242
Digital Object Identifier: 10.1305/ndjfl/1012429718

Subjects:
Primary: 03E25
Secondary: 03E35, 54Gxx

Rights: Copyright © 1999 University of Notre Dame

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Vol.40 • No. 4 • Fall 1999
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