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The Open Mapping and Closed Graph Theorem for Embeddable Topological Semigroups

Published online by Cambridge University Press:  20 November 2018

Douglass L. Grant
Douglass L. Grant*
Affiliation:
College of Cape Breton, Sydney, Nova Scotia
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Abstract

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Some extensions of the open mapping and closed graph theorem are proved for certain classes of commutative topological semigroups, namely those embeddable as open subsets of topological groups. Preliminary results of independent interest include investigations of properties which “lift” from embeddable semigroups to the groups in which they are embedded, and from semigroup homomorphisms to homomorphisms of the groups.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 5 , 01 December 1975, pp. 671 - 674
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Christoph, F. T. Jr, Free Topological Semigroups and Embedding Topological Semigroups in Topological Groups, Pac. J. Math., 34 (1970), p. 343.Google Scholar
2. Dugundji, J., Topology, Allyn and Bacon, Boston, 1966.Google Scholar
3. Gelbaum, B., Kalisch, G. K. and Olmsted, J. M. H., Embedding Semigroups and Integral Domains, Proc. Amer. Math. Soc, 2 (1951), p. 807.Google Scholar
4. Grant, D. L., Topological Groups which Satisfy an Open Mapping Theorem, submitted to Pac. J. Math.Google Scholar
5. Husain, T., Introduction to Topological Groups, Saunders, Philadelphia, 1966.Google Scholar
6. Husain, T., On a Closed Graph Theorem for Topological Groups, Proc. Jap. Acad., 44 (1968), p. 446.Google Scholar
7. McKilligan, S. A., Embedding Topological Semigroups in Topological Groups, Proc. Edinburgh Math. Soc, 17 (1970), p. 126.Google Scholar
8. Numakura, K., On Bicompact Semigroups, Math. J. Okayama Univ., 1 (1952), p. 99.Google Scholar
9. Rothman, N. J., Embedding of Topological Semigroups, Math. Ann., 139 (1960), p. 197.Google Scholar