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### The singular cubical set of a topological space

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UNSPECIFIED.
(1999)
*The singular cubical set of a topological space.*
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 126
(Part 1).
pp. 149-154.
ISSN 0305-0041

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## Abstract

For any topological space X let C(X) be the realization of the singular cubical set of X; let * 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 x C(*) 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 x C(*).

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Journal or Publication Title: | MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY |

Publisher: | CAMBRIDGE UNIV PRESS |

ISSN: | 0305-0041 |

Official Date: | January 1999 |

Volume: | 126 |

Number: | Part 1 |

Number of Pages: | 6 |

Page Range: | pp. 149-154 |

Publication Status: | Published |

URI: | http://wrap.warwick.ac.uk/id/eprint/14783 |

Data sourced from Thomson Reuters' Web of Knowledge

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