Vol. 57, No. 2, 1975

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Images and pre-images of localization maps

Arthur Herbert Copeland, Jr. and Albert Oscar Shar

Vol. 57 (1975), No. 2, 349–358
Abstract

This paper treats the induced function : [X,Y ] [X,Y P] when X and Y are spaces having “just enough” structure and : Y Y P is a localization map. Special attention is paid to the images of finite subsets of [X,Y ] and the preimages of finite subsets of [X,Y P]. While our results are not restricted to finite [X,Y ] we do, as an immediate corollary of our main theorem, establish necessary and sufficient conditions for the finiteness of [X,Y P].

Mathematical Subject Classification
Primary: 55D99
Milestones
Received: 4 October 1974
Revised: 7 February 1975
Published: 1 April 1975
Authors
Arthur Herbert Copeland, Jr.
Albert Oscar Shar