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A Topological Characterization of Gleason Parts of Real Function Algebras

Published online by Cambridge University Press:  20 November 2018

S. H. Kulkarni  and
B. V. Limaye
S. H. Kulkarni
Affiliation:
Department of Mathematics, Indian Institute of TechnologyPowai, Bombay 400 076, India
B. V. Limaye
Affiliation:
Department of Mathematics, Indian Institute of TechnologyPowai, Bombay 400 076, India
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Abstract

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It is well-known that a topological space is a Gleason part of some complex function algebra if and only if it is completely regular and σ-compact. In the present paper, a Gleason part of a real function algebra is characterized as a completely regular σ-compact topological space which admits an involutoric homeomorphism.

Keywords

46J10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 1 , 01 March 1983 , pp. 44 - 49
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Garnett, J., A topological characterization of Gleason parts, Pacific J. Math., 20 (1967), 59-63.Google Scholar
2. Kulkarni, S. H. and Limaye, B. V., Gleason parts of real function algebras, Canadian J. Math. 33 (1981), 181-200.Google Scholar