## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- 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

### On the connectedness properties of suns in finite dimensional spaces

#### 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

**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