Coincidence of the Isbell and fine Isbell topologies |
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Authors: | Francis Jordan |
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Institution: | Department of Mathematics and Computer Science, Queensborough Community College, Queens, NY 38677, United States |
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Abstract: | Let C(X,Y) be the set of all continuous functions from a topological space X into a topological space Y. We find conditions on X that make the Isbell and fine Isbell topologies on C(X,Y) equal for all Y. For zero-dimensional spaces X, we show there is a space Z such that the coincidence of the Isbell and fine Isbell topologies on C(X,Z) implies the coincidence on C(X,Y) for all Y. We then consider the question of when the Isbell and fine Isbell topologies coincide on the set of continuous real-valued functions. Our results are similar to results established for consonant spaces. |
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Keywords: | Function space Compact-open topology Isbell topology Finest splitting topology Upper semicontinuous |
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