Vol. 47, No. 2, 1973

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ISSN: 0030-8730
Dimension theory in zero-set spaces

M. J. Canfell

Vol. 47 (1973), No. 2, 393–400
Abstract

The main purpose of this paper is to show that the zero-set spaces of Gordon provide a natural and very general setting in which to develop dimension theory. Defining covering dimension for zero-set spaces in the natural way, it is shown that the subspace theorem, the product theorem, and sum theorem hold. As a consequence it is possible to give a subspace theorem for arbitrary topological spaces.

Mathematical Subject Classification 2000
Primary: 54F45
Secondary: 54C50
Milestones
Received: 2 June 1972
Revised: 11 October 1972
Published: 1 August 1973
Authors
M. J. Canfell