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The Fell Topology on C(X)
Author(s) -
HOLÁ L̆BICA,
MCCOY R. A.
Publication year - 1992
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1992.tb32253.x
Subject(s) - hyperspace , topology (electrical circuits) , social connectedness , hausdorff space , topological space , mathematics , space (punctuation) , isolated point , general topology , compact space , continuous functions on a compact hausdorff space , locally compact space , normal space , combinatorics , pure mathematics , topological vector space , computer science , psychotherapist , operating system , psychology
The space C(X, Y) of continuous functions from a topological space X to a Hausdorff space Y can be thought of as a subset of the hyperspace of closed subsets of X × Y by identifying each element of C(X, Y) with its graph. A study is made of C(X, Y) with the topology inherited by the Fell topology on hyperspaces. The emphasis is on real‐valued functions where Y =ℝ, in which case the function space is denoted by C(X) . A number of characterizations are given of topological properties of C(X) and C(X, Y) in terms of properties on X (and Y ). These properties often turn out to involve both local compactness and connectedness type of conditions.