Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T02:30:54.990Z Has data issue: false hasContentIssue false

Countable sum theorem for locally closed sets

Published online by Cambridge University Press:  17 April 2009

Satya Deo
Affiliation:
Department of Mathematics, University of Jammu, Jammu 180001, India.
Dalip Singh Jamwal
Affiliation:
Department of Mathematics, University of Jammu, Jammu 180001, India.
Rights & Permissions [Opens in a new window]

Abstract

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.

In this paper we show that the countable sum theorem for locally-closed sets, for sheaf theoretic cohomological dimension over a given ring L, holds in all perfectly normal spaces as well as in all locally compact spaces.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Bourbaki, Nicolas, Elements of mathematics. General topology (Hermann, Paris; Addison-Wesley, Reading, Massachusetts; Palo Alto; London; 1966).Google Scholar
[2]Bredon, Glen E., Sheaf theory (McGraw-Hill, New York, Toronto, London, 1968).Google Scholar
[3]Deo, Satya, “One dimension manifold is of cohomological dimension two”, Proc. timer. Math. Soc. 52 (1975), 445446.CrossRefGoogle Scholar
[4]Deo, Satya, “Cohomological dimension of a n-manifold is n + 1”, Pacific J. Math. 67 (1976), 155160.CrossRefGoogle Scholar
[5]Deo, Satya and Shukla, Ram Anugrah, “On cohomological dimension and the sum theorems”, Acta Math. Acad. Sci. (to appear).Google Scholar
[6]Nagami, Keiô, Dimension theory (Pure and Applied Mathematics, 37. Academic Press, New York and London, 1970).Google Scholar