Proceedings of the Centre for Mathematics and its Applications

On the connectedness properties of suns in finite dimensional spaces

A. L. Brown

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Abstract

The author introduced in [3] the notion of an M-con~ected closed subset of a norrned linear space and defined the class of (BM)-spaces. An M-connected closed subset of a finite dimensional normed linear space is a sun and a sun in a space which is either of dimension two or is a finite dimensional (m>i)-space is M-connected. Theorem 1 asserts that an M-connected closed subset of a finite dimensional space is n-connected for all n = 0,1,2 .... Theorem 2 relates Tl1eorem 1 to the results of [3]. Theorem 3 is an improvement of a result of Koshcheev and asserts that a sun in a finite dimensional space is path-connected.

Article information

Source
Workshop/Miniconference on Functional Analysis and Optimization. Simon Fitzpatrick and John Giles, eds. Proceedings of the Centre for Mathematical Analysis, v. 20. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1988), 1-15

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416340097

Mathematical Reviews number (MathSciNet)
MR1009588

Zentralblatt MATH identifier
0682.41040

Citation

Brown, A. L. On the connectedness properties of suns in finite dimensional spaces. Workshop/Miniconference on Functional Analysis and Optimization, 1--15, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1988. https://projecteuclid.org/euclid.pcma/1416340097


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