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Krasnosel'skii Theorems for Non-Separating Compact Sets

Published online by Cambridge University Press:  20 November 2018

N. Stavrakas
N. Stavrakas*
Affiliation:
University of North Caroline, Charlotte, N.C.282223
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Abstract

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Let S ⊂ Rd, d ≥ 2, be compact and let E denote the set (d — 2) — extreme points of S. M. Breen has shown that if E is countable and S ≠ E, then S is planar. A new proof of this result is given as well as a Krasnosl'skii theorem for (d - 2) extreme points which combines and generalizes previous results.

Keywords

Primary 52A30Secondary 52A20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 2 , 01 June 1983 , pp. 247 - 249
Copyright
Copyright © Canadian Mathematical Society 1983

References

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3. Goodey, P. R., A note on starshaped sets, Pacific J. Math., vol 61 (1975) pp 151–152.Google Scholar
4. Stavrakas, N., A note on starshaped sets, (k)-extreme points and the half-ray property Pacific J. Math., vol 53 (1974) pp 627–628.Google Scholar