Mathematika

Table of Contents - June 1974 - Volume 21, Issue 01  

Research Article

Families of compact sets and their universals

A. J. Ostaszewskia1

a1 Mathematics Department, The University, Leicester LEI 7RH.

§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

S0025579300005878_eqn1

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 . To define these let us make the convention that, for D [0, 1] × X, we write

S0025579300005878_eqnU1

D is said to be universal for if

S0025579300005878_eqnU2

(Received January 02 1974)

Key Words:

  • 54H05: GENERAL TOPOLOGY; Connections with other structures; Descriptive set theory.