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Gelfand dualities over topological fields

Part of: Categories with structure General theory of categories and functors Special categories

Published online by Cambridge University Press:  09 April 2009

Brian J. Day
Brian J. Day
Affiliation:
School of Mathematics and Physics, Macquarie University, North Ryde, NSW 2113, Australia
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Abstract

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The spectral duality theory of H.-E. Porst and M. B. Wischnewsky is examined in more generality, and examples based on topological fields are described.

MSC classification

Secondary: 18A40: Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) 18B30: Categories of topological spaces and continuous mappings 18D20: Enriched categories (over closed or monoidal categories)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 2 , April 1982 , pp. 171 - 177
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Binz, E., Continuous convergence on C(X), Lecture Notes in Mathematics 469 (Springer-Verlag, Berlin, Heidelberg, New York, 1975).CrossRefGoogle Scholar
[2]Cornish, W. H., ‘Amalgamating commutative regular rings’, Comment. Math. Univ. Carolinae, 18–3 (1977), 423–436.Google Scholar
[3]Day, B. J., ‘Note on duality of Kelleyspace products’, Bull. Austral. Math. Soc. 19 (1978), 273–275.CrossRefGoogle Scholar
[4]Day, B. J., ‘An extension of Pontryagin duality’, Bull. Austral. Math. Soc. 19 (1978), 445–456.CrossRefGoogle Scholar
[5]Hong, S. S. and Nel, L. D., ‘Duality theorems for algebras in convenient categories’, Math. Z. 166 (1979), 131–136.CrossRefGoogle Scholar
[6]Kaplan, S., ‘Extensions of the Pontryagin duality II: Direct and inverse sequences’, Duke Math. J. 17 (1950), 419–435.CrossRefGoogle Scholar
[7]Kelly, G. M., ‘Monomorphisms, epimorphisms, and pull-backs’, J. Austral. Math. Soc. 9 (1969), 124–142.CrossRefGoogle Scholar
[8]Porst, H.-E. and Wischnewsky, M. B., ‘Every topological category is convenient for Gelfand duality’, Manuscripta Math. 25 (1978), 169–204.CrossRefGoogle Scholar