Vol. 98, No. 1, 1982

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Approximating compact sets in normed linear spaces

Jack Emile Girolo

Vol. 98 (1982), No. 1, 81–89

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
Received: 3 September 1980
Published: 1 January 1982
Jack Emile Girolo