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A Moore Strongly Rigid Space

Published online by Cambridge University Press:  20 November 2018

V. Tzannes
V. Tzannes*
Affiliation:
Department of Mathematics, University of Patras, Fatras, Greece
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Abstract

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It is proved that for every Hausdorff space ℝ and for every Hausdorff (regular or Moore) space X, there exists a Hausdorff (regular or Moore, respectively) space S containing X as a closed subspace and having the following properties:

  • la) Every continuous map of S into ℝ is constant.

  • b) For every point x of S and every open neighbourhood U of x there exists an open neighbourhood V of x, V ⊆ U such that every continuous map of V into ℝ is constant.

  • 2) Every continuous map f of S into S (f ≠ identity on S) is constant.

In addition it is proved that the Fomin extension of the Moore space S has these properties.

Keywords

54G9954C0554D1054D15EmbeddingHausdorffRegularMooreFominStrongly rigid spaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 4 , 01 December 1991 , pp. 547 - 552
Copyright
Copyright © Canadian Mathematical Society 1991

References

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