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Families of compact sets and their universals

Part of: Connections with other structures, applications

Published online by Cambridge University Press:  26 February 2010

A. J. Ostaszewski
A. J. Ostaszewski
Affiliation:
Mathematics Department, The University, Leicester LEI 7RH.
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Extract

§1. Introduction and Summary. Throughout X is a complete separable metric space. We write K1 for the family of non-empty compact subsets of X. K1 may be endowed with a metric (first introduced by Hausdorff) under which K1 is complete and separable. We shall make use of the subbase for this metrizable topology of K1 given by sets of the two forms

for U open in X (see Kuratowski [4] or E. Michael [9] for a discussion of topologies on the space of subsets of X). if we shall be concerned with sets in [0, 1] × X which are universal for ℋ. To define these let us make the convention that, for D ⊆ [0, 1] × X, we write

D is said to be universal for ℋ if

MSC classification

Secondary: 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
Type
Research Article
Information
Mathematika , Volume 21 , Issue 1 , June 1974 , pp. 116 - 127
Copyright
Copyright © University College London 1974

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References

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