Hostname: page-component-6898cfcb55-w5hgh Total loading time: 0 Render date: 2026-11-11T21:15:17.211Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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

Information

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

References

1. Brandenburg, H. and Mysior, A., For every Hausdorff space Y there exists a non-trivial Moore space on which all continuous functions into Y are constant, Pacific J. of Mathematics (1)111 (1984), 1–8.Google Scholar
2. de, J. Groot, Groups represented by homeomorphism groups, I, Math. Ann. 138 (1959), 80–102.Google Scholar
3. Iliadis, S. and Tzannes, V., Spaces on which every continuous map into a given space is constant, Canad. J. Math. 6 (1986), 1281–1296.Google Scholar
4. Kannan, V. and Rajagopalan, M., Constructions and applications of rigid spaces, II, Amer. J. Math. (6)100 (1978), 1139–1172.Google Scholar
5. Porter, J. and Votaw, C., H-closed extensions, II,Trans.Am. Math. Soc. 202 (1975), 193–209.Google Scholar