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1 Journal of Applied Analysis

1 2010

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Čech-completeness and related properties of the generalized compact-open topology

Holá L`., Zsilinszky L.

Journal of Applied Analysis

2010

Vol. 16, nr 1

151-169

The generalized compact-open topology τc on partial continuous functions with closed domains in X and values in Y is studied. If Y is a non-countably compact Čech-complete space with a Gδ-diagonal, then τc is Čech-complete, sieve complete and satisfies the p-space property of Arhangel'skii, respectively, if and only if X is Lindelof and locally compact. Lindelofness, paracompactness and normality of τc is also investigated. New results are obtained on Čech-completeness, sieve completeness and the p-space property for the compact-open topology on the space of continuous functions with a general range Y.