Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-14T01:20:22.899Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximal inverse subsemigroups of S(X)

Published online by Cambridge University Press:  18 May 2009

Bridget B. Baird
Bridget B. Baird
Affiliation:
Department of Mathematics University of Florida Gainesville, Florida 32611
Rights & Permissions [Opens in a new window]

Extract

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.

If X is a topological space then S(X) will denote the semigroup, under composition, of all continuous functions from X into X. An element f in a semigroup is regular if there is an element g such that fgf = f. The regular elements of S(X) will be denoted by R(X). Elements f and g are inverses of each other if fgf = f and gfg = g. Every regular element has an inverse [1]. If every element in a semigroup has a unique inverse then the semigroup is an inverse semigroup. In this paper we examine maximal inverse subsemigroups of S(X).

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 24 , Issue 1 , January 1983, pp. 53 - 64
Copyright
Copyright © Glasgow Mathematical Journal Trust 1983

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Math. Surveys 7, Amer. Math. Soc. (Providence R. I., I (1961), II (1967)).Google Scholar
2.Hofer, R. D., Restrictive semigroups of continuous selfmaps on arcwise connected spaces. Proc. London Math. Soc. (3) 25 (1972), 358–384.CrossRefGoogle Scholar
3.Magill, K. D. Jr, and Subbiah, S., Green's relations for regular elements of semigroups of endomorphisms, Canad. J. Math. 26 (1974), 1484–1497.CrossRefGoogle Scholar
4.Nichols, J. W., A class of maximal inverse subsemigroups of T x, Semigroup Forum 13 (1976), 187–188.CrossRefGoogle Scholar
5.Reilly, N. R., Maximal inverse subsemigroups of T x, Semigroup Forum 15 (1978), 319–326.CrossRefGoogle Scholar
6.Reilly, N. R., Transitive inverse semigroups on compact spaces, Semigroup Forum 8 (1974), 184–187.CrossRefGoogle Scholar
7.Schein, B. M., A symmetric semigroup of transformations is covered by its inverse subsemigroups, Aero. Math. Acad. Sci. Hungar. 22 (1971), 163–171 (Russian).Google Scholar