A Note on Cartesian Products

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1969Publisher:JSTORJournal:American Journal of Mathematics, volume 91, page 32 (issn: 0002-9327,

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Authors: Brown, Morton;

doi: 10.2307/2373266

A Note on Cartesian Products

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Abstract

0. Introduction. Let as be an arc in the interior In of the n-cell In and let X be the quotient space I"/ac obtained by shrinking a to a point. According to Kwun and Raymond [4], X X 12 is an (n + 2)-cell. The crucial tool in their proof is the result of Andrews-Curtis that, under the above conditions, In/a X R1 is homeomorphic to In XR1. The purpose if this paper is to prove by completely elementary means (i. e. avoiding the Andrews-Curtis theorem and the theory of generalized manifolds) a more general result which specializes to the following:

Keywords

topology

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