Vol. 117, No. 1, 1985

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ISSN: 0030-8730
The extension of equi-uniformly continuous families of mappings

Ronald Fred Levy and Michael David Rice

Vol. 117 (1985), No. 1, 149–161
Abstract

In previous papers, we discussed the extension of uniformly continuous real-valued mappings from subspaces of metric spaces and the same question for mappings into certain Banach spaces, such as c0(I) and l(I). Since the extension of uniformly continuous mappings into l(I) is equivalent to the extension of equi-uniformly continuous point bounded families of real-valued mappings, it is natural to ask about the extension of equi-uniformly continuous families which are not necessarily point-bounded. The present paper investigates this extension property and several related questions concerning the extension of uniformly continuous mappings with values in uniformly discrete spaces.

Mathematical Subject Classification 2000
Primary: 54C30
Secondary: 54E15
Milestones
Received: 8 April 1983
Revised: 27 June 1983
Published: 1 March 1985
Authors
Ronald Fred Levy
Michael David Rice