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On transfinite inductive dimension and deficiency modulo a class P

✍ Scribed by M.G. Charalambous

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
873 KB
Volume
81
Category
Article
ISSN
0166-8641

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✦ Synopsis

We establish some fundamental properties of transfinite inductive dimension module a class 7J and use them to compute the dimensions of Bernstein sets and other pathological spaces. We show that transfinite completeness degree and transfinite completeness deficiency do not agree on separable metrizable spaces. We construct a separable compact space that contains an co-Inductionally embedded discrete subspace, which answers a question of .

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## Abstract Let 1 < __s__ < 2, __λ~k~__ > 0 with __λ~k~__ → ∞ satisfy __λ__~__k__+1~/__λ~k~__ ≥ __λ__ > 1. For a class of Besicovich functions __B__(__t__) = $ \sum ^{\infty} \_{k=1} \, \lambda ^{s-2} \_{k} $ sin __λ~k~t__, the present paper investigates the intrinsic relationship between box dimen