Approximating compact sets in normed linear spaces

Jack Emile Girolo

Vol. 98 (1982), No. 1, 81–89

DOI: 10.2140/pjm.1982.98.81

Abstract

It is shown that in normed linear spaces compact sets can be approximated by compact absolute neighborhood retracts in the following sense: If X is a compact subset of a normed linear space, then for every 𝜀 > 0 there exists a compact absolute neighborhood retract that contains X and has the property that each point of the retract is within 𝜀 of X. If the choice of 𝜀 is sufficiently large, the retract can be chosen to be an absolute retract.

Mathematical Subject Classification 2000

Primary: 54F40, 54F40

Secondary: 41A65, 46B20

Milestones

Received: 3 September 1980

Published: 1 January 1982