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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spaces in which the nondegenerate connected sets are the cofinite sets


Author: Gary Gruenhage
Journal: Proc. Amer. Math. Soc. 122 (1994), 911-924
MSC: Primary 54D05; Secondary 54A35, 54G20
MathSciNet review: 1287102
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Abstract: Assuming the continuum hypothesis (CH), we construct a perfectly normal space X such that $ Y \subset X$ is connected and nondegenerate iff $ X\backslash Y$ is finite. We also show that completely regular, as well as countable Hausdorff, examples of this kind can be obtained under axioms weaker than CH, e.g., Martin's Axiom.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1287102-2
PII: S 0002-9939(1994)1287102-2
Article copyright: © Copyright 1994 American Mathematical Society