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Complete metrizability of generalized compact-open topology

✍ Scribed by L'. Holá

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
602 KB
Volume
91
Category
Article
ISSN
0166-8641

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✦ Synopsis

Let X and Y be Hausdorff topological spaces. Let P be the family of all partial maps from X to Y: a partial map is a pair (B,f).

where B E CL(X) (= the family of all nonempty closed subsets of X) and f is a continuous function from B to El'. Denote by 7~ the generalized compact-open topology on P. We show that if X is a hemicompact metrizable space and Y is a FrCchet space. then (P. TC) is completely metrizable and homeomorphic to a closed subspace of (CL(X), TF) x (C(X. Y). T~,cJ), where T,T is the Felt topology on CL(X) and 71'0 is the compact-open topology on C(X, Y).

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