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The Katětov-Morita theorem for the dimension of metric frames

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  • D. Brijlall

    (University of KwaZulu-Natal
    University of KwaZulu-Natal)

  • D. Baboolal

    (University of KwaZulu-Natal
    University of KwaZulu-Natal)

Abstract

The results which appear here are devoted to the dimension theory of metric frames. We begin by characterizing the covering dimension dim of metric frames in terms of special sequences of covers and then prove the fundamental Katětov-Morita Theorem asserting that Ind L = dim L for every metric frame L. Next, we establish two characterizations of the dimension function Ind in metric frames, one in terms of special bases and another in terms of decompositions into subspaces of dimension zero. These characterizations yield a sum theorem.

Suggested Citation

  • D. Brijlall & D. Baboolal, 2010. "The Katětov-Morita theorem for the dimension of metric frames," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(3), pages 535-553, June.
    • Handle: RePEc:spr:indpam:v:41:y:2010:i:3:d:10.1007_s13226-010-0025-x
    DOI: 10.1007/s13226-010-0025-x
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    Keywords

    Dimension; metric frames;

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