The Cluster Function of Single-Valued Functions

Author： Richter Christian  

Publisher： Springer Publishing Company

ISSN： 0927-6947

Source： Set-Valued Analysis, Vol.14, Iss.1, 2006-03, pp. : 25-40

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Abstract

Given a single-valued function f between topological spaces X and Y, we interpret the cluster set C(f;X) as a multivalued function f=C(f;⋅) associated to f - the cluster function of f. For appropriate metrizable spaces X and Y, we characterize cluster functions C(f;⋅) among arbitrary set-valued functions f and show that every cluster function f=C(f;⋅) admits a selection h of Baire class 2 such that f=C(h;⋅).

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