An infraconsonant nonconsonant completely regular space |
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Authors: | Francis Jordan |
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Institution: | Department of Mathematics and Computer Science, Queensborough Community College, Queens, NY, USA |
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Abstract: | Let R denote the real numbers. We construct in ZFC a countable space X such that X has exactly one non-isolated point, X is infraconsonant, and X is not consonant. We conclude that X is a completely regular space such that Isbell topology on C(X,R) is a group topology that coincides with the natural (finest splitting) topology on C(X,R), but the Isbell and compact-open topologies on C(X,R) do not coincide. The example answers two open problems in the literature. |
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Keywords: | primary 26A15 secondary 54A25 |
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