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Dr. Ismail Ahmed Mahmoud Abdelaziz Ibedou :: Publications:
GT21/2-spaces, GT5-spaces and GT6-spaces, Submitted to: Journal of King Saud University, www.ksu.edu.sa.
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|Full paper||Ismail Ahmed Mahmoud Abdelaziz Ibedou_PAPER_11.pdf|
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In this paper we obtain a modified version of the classical theorem of Pontrjagin and Schnirelmann concerning the covering dimension of a compact metric space and the box-counting dimensions associated with the metrics on the space. T. Miyata and T. Watanabe defined box-counting dimension for approximate sequences X which represent compact metric spaces X as approximate resolutions p : X → X. We show that the covering dimension equals the infimum of the box-counting dimensions associated with the approximate resolutions of the space.