Vol. 23, No. 3, 1967

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Unstable points in the hyperspace of connected subsets

Neil Robert Gray

Vol. 23 (1967), No. 3, 515–520

A topological property which has proved useful is that of possessing an unstable point. It is thus interesting to see which topological spaces consist entirely of unstable points. The purpose of this paper is to describe a class of such spaces. This is done in the

Theorem. If X is a finite simplicial complex then the hyperspace C(X) consists entirely of unstable points if and only if X has no free l-simplex.

The proof given here is for the case where X is connected —the more general theorem follows obviously from this case.

Mathematical Subject Classification
Primary: 54.55
Received: 27 January 1967
Published: 1 December 1967
Neil Robert Gray