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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.
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Abstract

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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

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