Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-22T20:55:39.822Z Has data issue: false hasContentIssue false
  • English
  • Français

Homomorphic images of restrictive star semigroups

Published online by Cambridge University Press:  18 May 2009

Kenneth D. Magill Jr
Kenneth D. Magill Jr
Affiliation:
State University of New York at Buffalo, and University of Leeds
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.

Let Y be a subspace of a topological space X. Then S(X, Y) denotes the semigroup, under composition, of all continuous selfmaps of X which also carry Y into Y. In the special case Y = X, the simpler notation S(X)is used. We have devoted several recent papers ([4], [7] and [8]) to the problem of determining when S(Z) and S(X, Y)are isomorphic and, more generally, when S(Z) is a homomorphic image of S(X, Y). In this paper, we investigate the analogous problem for certain semigroups of functions on spaces which were introduced in [5]. These include semigroups of closed functions which are treated in further detail.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 11 , Issue 1 , January 1970 , pp. 58 - 71
Copyright
Copyright © Glasgow Mathematical Journal Trust 1970

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Amer. Math. Soc. Mathematical Surveys 7, Vols I and II (Providence, R.I., 1961 and 1967).Google Scholar
2.Kuratowski, C., Topologie II (Warsaw, 1950).Google Scholar
3.Ljapin, E. S., Semigroups, Amer. Math. Soc. Translations of Mathematical Monographs 3 (Providence, R.I., 1963).Google Scholar
4.Magill, K. D. Jr, Subsemigroups of S(X), Math. Japon. 11 (1966), 109–115.Google Scholar
5.Magill, K. D. Jr, Semigroup structures for families of functions, III; Rr*-semigroups, J. Australian Math. Soc. 14, part 4 (1967), 524–538.Google Scholar
6.Magill, K. D. Jr, Restrictive semigroups of closed functions, Canad. J. Math., 20 (1968), 1215–1229.Google Scholar
7.Magill, K. D. Jr, Homomorphic images of certain semigroups of continuous functions, Math. Japon. 13 (1968), 133–141.Google Scholar
8.Magill, K. D. Jr, Homomorphisms and semigroups of continuous functions, Proc. Topology Conference (Kanpur, India, 10 1968); to appear.Google Scholar
9.Sierpinski, W., General topology (Toronto, 1952).Google Scholar