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Hausdorff Dimension in Convex Bornological Spaces

✍ Scribed by J. Almeida; L. Barreira

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
106 KB
Volume
268
Category
Article
ISSN
0022-247X

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✦ Synopsis

For non-metrizable spaces the classical Hausdorff dimension is meaningless. We extend the notion of Hausdorff dimension to arbitrary locally convex linear topological spaces and thus to a large class of non-metrizable spaces. This involves a limiting procedure using the canonical bornological structure. In the case of normed spaces the new notion of Hausdorff dimension is equivalent to the classical notion.  2002 Elsevier Science (USA)

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