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Spaces in Which the Nondegenerate Connected Sets Are the Cofinite Sets

Gary Gruenhage
Proceedings of the American Mathematical Society
Vol. 122, No. 3 (Nov., 1994), pp. 911-924
DOI: 10.2307/2160772
Stable URL: http://www.jstor.org/stable/2160772
Page Count: 14
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Spaces in Which the Nondegenerate Connected Sets Are the Cofinite Sets
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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 $\operatorname{iff} X\backslash Y$ 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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