Vol. 15, No. 4, 1965

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Fixed points in a transformation group

Hsin Chu

Vol. 15 (1965), No. 4, 1131–1135
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
Authors
Hsin Chu