Vol. 25, No. 2, 1968

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ISSN: 0030-8730
Mappings and dimension in general metric spaces

James Edgar Keesling

Vol. 25 (1968), No. 2, 277–288
Abstract

In this paper necessary and sufficient conditions are developed for certain classes of continuous functions f(X) = Y , where X and Y are arbitrary metric spaces, to have the property that dimK = dimf(K) for all closed K X. In particular it is shown that if f is closed and dimf(K) > dimK for some closed K X, then there exists a closed K′⊂ X so that dimK= 0 and dimf(K) > 0. These results are then used to show that if f is closed and finite to one so that the multiplicity function of f takes on at most k + 1 distinct values, then dimK dimf(K) dimK + k for all closed K X.

Mathematical Subject Classification
Primary: 54.60
Milestones
Received: 19 May 1967
Published: 1 May 1968
Authors
James Edgar Keesling