Fixed points in a transformation group

Hsin Chu

Vol. 15 (1965), No. 4, 1131–1135

DOI: 10.2140/pjm.1965.15.1131

Abstract

In this paper, the following result is proved: “Let (X,T,π) be a transformation group, where X is a Peano continuum with an end point fixed under T. If the group T is one of the following two types: (1) It contains a subgroup Rⁿ such that G∕Rⁿ is compact or (2) It contains a s subgroup Z ⋅ Rⁿ such that G∕(Z ⋅ Rⁿ) is compact, where Z is isomorphic to the discrete additive group of all integers, then T has another fixed point.”

Mathematical Subject Classification

Primary: 54.80

Secondary: 22.40

Milestones

Received: 8 June 1964

Published: 1 December 1965