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On Topological Algebra Bundles

Part of: Fiber spaces and bundles Methods of category theory in functional analysis Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

Athanasios Kyriazia
Athanasios Kyriazia
Affiliation:
Mathematical InstituteUniversity of Athens57, Solonos Street GR-106 79 Athens, Greece
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Abstract

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Topological algebra bundles whose fibre (-algebras) admit functional representations constitute a category, antiequivalent with that of (topological) fibre bundles having completely regular bundle spaces and locally compact fibres.

Keywords

topological algebra bundlealgebraic chartalgebraic atlassystem of transition functions(X-algebra), spectrum bundlespectrum functorlocally m-convex algebra bundlefunctional representationscategory antiequivalencespectrum of a topological algebraWaelbroeck algebraGel'fand-Mazur (topological) algebra.

MSC classification

Secondary: 46H05: General theory of topological algebras 46M20: Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) 55R05: Fiber spaces 55R10: Fiber bundles
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 3 , December 1987 , pp. 398 - 419
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Atiyah, M. F., K-Theory (Benjamin, New York, 1967).Google Scholar
[2]Bourbaki, N., General Topology I (Hermann, Paris, 1966).Google Scholar
[3]Bourbaki, N., General Topology II (Hermann, Paris, 1966).Google Scholar
[4]Dugundji, J., Topology (Allyn and Bacon, Boston, Mass., 1970).Google Scholar
[5]Gelbaum, B. R., ‘Banach algebra bundles’, Pacific J. Math. 28 (1969), 337–349.Google Scholar
[6]Galbaum, B. R. and Kyriazis, A., ‘Fibre tensor product bundles’, Proc. Amer. Math. Soc. 93 (1985), 675–680.Google Scholar
[7]Karoubi, M., K-Theory (Springer-Verlag, Berlin, 1978).Google Scholar
[8]Kyriazis, A., ‘On the spectra of topological -tensor product -algebras’, Yokohama Math. J. 31 (1983), 47–65.Google Scholar
[9]Mallios, A., Topological Algebras: Selected Topics (North-Holland, Amsterdam, 1986).Google Scholar
[10]Mallios, A., ‘On functional representations of topological algebras’, J. Fund. Anal. 6 (1970), 468–480.Google Scholar
[11]Mallios, A., ‘Vector bundles and k-theory over topological algebras’, J. Math. Anal. Appl. 92 (1983), 452–506.CrossRefGoogle Scholar
[12]Mallios, A., ‘Continuous vector bundles over topological algebras’, J. Math. Anal. Appl. 113 (1986), 245–254.CrossRefGoogle Scholar