Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-25T00:44:44.683Z Has data issue: false hasContentIssue false
  • English
  • Français

Inverse limit theorem and expansion theorem for cohomological dimension

Published online by Cambridge University Press:  17 April 2009

Satya Deo  and
Subhash Muttepawar
Satya Deo
Affiliation:
Department of Mathematics, University of Jammu, Canal Road, Jammu 180001, India.
Subhash Muttepawar
Affiliation:
Department of Mathematics, University of Jammu, Canal Road, 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.

For a given ground ring L, let dimL(X) denote the sheaf theoretic cohomological dimension of a space X. In this paper we prove an inverse limit theorem for this dimension function. Then we apply this theorem to show that for a large classs of rings the Freudenthal's expansion theorem, expressing a compact metric space X of dimL(X) as the inverse limit of an system of compact polyhedra Kα of dimL(Kα), is not valid.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1983 , pp. 67 - 75
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Bredon, Glen E., Sheaf theory (McGraw-Hill, New York, Toronto, London, 1968).Google Scholar
[2]Charalambous, M.G., “The dimension of inverse limit and N-compact spaces”, Proc. Amer. Math. Soc. 85 (1982), 648–652.Google Scholar
[3]Deo, Satya, “A one dimensional manifold is of cohomological dimension 2”, Proc. Amer. Math. Soc. 52 (1975), 445–446.Google Scholar
[4]Deo, Satya, “The cohomological dimension of a n-manifold is n + 1”, Pacific J. Math. 67 (1976), 155–160.CrossRefGoogle Scholar
[5]Deo, Satya and Shukla, R.A., “On sum theorems of cohomological dimension”, Acta Math. Acad. Sci. Hungar (to appear).Google Scholar
[6]Katuta, Yûkiti, “On the covering dimension of inverse limits”, Proc. Amer. Math. Soc. 84 (1982), 588–592.Google Scholar
[7]Mardeŝić, Sibe, “On covering dimension and inverse limits of compact spaces”, Illinois J. Math. 4 (1960), 278–291.CrossRefGoogle Scholar
[8]Nagami, Keiô, “Dimension of non-normal spaces”, Fund. Math. 109 (1980). 113–121.CrossRefGoogle Scholar
[9]Pears, A.R., Dimension theory of general spaces (Cambridge University Press, England, New York, Melbourne, 1975).Google Scholar