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On the relationship between ordinary thin sets and full-thin sets

Published online by Cambridge University Press:  09 April 2009

J. S. Hwang  and
H. L. Jackson
J. S. Hwang
Affiliation:
Department of Mathematics McMaster UniversityHamilton, Ontario, Canada
H. L. Jackson
Affiliation:
Centre de Recherches Mathématiques Université de MontréalMontréal, QuébecCanada also Department of Pure Mathematics Australian National UniversityCanberra, A.C.T. 2600, Australia
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Abstract

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In this work we demonstrate that if Ω ⊂ Rn (n ≧ 3) is either a half space or a unit ball, and if E ⊂ ω then E is an ordinary thin set at a boundary point of Ω (including the point at infinity if Ω is a half space) if and only if it is a full-thin set at the corresponding Kuramochi boundary point of Ω. The case for n = 2 has already been considered in an earlier work.

1980 Mathematics subject classification (Amer. Math. Soc.): 31 B 05.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 3 , May 1980 , pp. 348 - 361
Copyright
Copyright © Australian Mathematical Society 1980

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