Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-11T00:04:20.501Z Has data issue: false hasContentIssue false
  • English
  • Français

Inverse semigroups of homeomorphisms between open subsets

Published online by Cambridge University Press:  09 April 2009

Bridget Bos Baird
Bridget Bos Baird
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida, U.S.A.
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.

The symbol IG(X) denotes the inverse semigroup, under composition of functions, of all homeomorphisms between open subsets of a T1 topological space X. The first result is that two such semigroups IG(X) and IG(Y) are isomorphic if and only if the spaces X and Y are homeomorphic. Ideals of IG(X) are next examined and it is shown that for many spaces X the semigroup IG(X) is 0-simple. We also look at congruences on IG(X); one result is that we determine a congruence which in many instances is the largest proper congruence on IG(X).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 1 , August 1977 , pp. 92 - 102
Copyright
Copyright © Australian Mathematical Society 1977

References

Clifford, A. H. and Preston, G. B. (1961, 1967), The Algebraic Theory of Semigroups, vol. I and II (American Math. Soc).Google Scholar
Preston, G. B. (1954), Inverse semigroups, J. London Math. Soc. 29, 396–403.CrossRefGoogle Scholar
Reilly, N. R. and Scheiblich, H. E. (1967), Congruences on regular semigroups, Pacific J. of Math. 23, 349–360.CrossRefGoogle Scholar
Scheiblich, H. E. (1973), Concerning congruences on symmetric inverse semigroups, Czechoslovak Math. J. 23, 1–10.CrossRefGoogle Scholar
Schein, B. M. (1965), Materials of the Second Baltic Geometric Conference, Tartu, 179–182.Google Scholar
Thron, W. J. (1962), Lattice-equivalence of topological spaces. Duke Mathematical J. 29, 671–679.CrossRefGoogle Scholar