Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T14:42:41.778Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
BERT WIEST
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK, e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)