## Abstract

Let G be a monotone decomposition of E^{n}, then G can be extended in a trivial way, to the monotone decomposition G^{1} of E^{n + 1}, where E^{n} = {{x_{1} … x_{n}, 0) ∈ E^{n + 1}}, by adding to G all points of E^{n + 1} − E^{n}. If the decomposition space E^{n}/G of G is homeomorphic to E^{n}, E^{n}\G is said to be obtained by a pseudoisotopy if there exists a map F: E^{n} × I→ E^{n} × I, such that F _{t}(=f/E^{n} × t) is homeomorphism onto E^{n} × 1, for all 0 ≦; 1 < 1, F_{0} is the identity and F_{1} is equivalent to the projection The purpose of this paper is to present a relation between these two notions. It will then follow, that if G is the decomposition of E^{3} to points, circles and figure-eights, due to R. H. Bing, for which E^{3}/G is homeomorphic to E^{3} then E^{4}/G^{1} is not homeomorphic to E^{4}.

Original language | English |
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Pages (from-to) | 727-729 |

Number of pages | 3 |

Journal | Pacific Journal of Mathematics |

Volume | 29 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1969 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics

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