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The singular cubical set of a topological space

Published online by Cambridge University Press:  01 January 1999

ROSA ANTOLINI  and
BERT WIEST
ROSA ANTOLINI
Affiliation:
Southbank International School, 36-38 Kensington Park Road, London W11 3BU, UK, e-mail: rosa@antolini.demon.co.uk
BERT WIEST
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK, e-mail: bertold@maths.warwick.ac.uk
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Abstract

For any topological space X let C(X) be the realization of the singular cubical set of X; let [midast ] be the topological space consisting of one point. In [1] Antolini proves, as a corollary to a general theorem about cubical sets, that C(X) and X×C([midast ]) are homotopy equivalent, provided X is a CW-complex. In this note we give a short geometric proof that for any topological space X there is a natural weak homotopy equivalence between C(X) and X×C([midast ]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 126 , Issue 1 , January 1999 , pp. 149 - 154
Copyright
The Cambridge Philosophical Society 1999

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