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.
Information
Published: 1 January 1988
First available in Project Euclid: 18 November 2014
zbMATH: 0682.41040
MathSciNet: MR1009588
Rights: Copyright © 1988, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.
