A Class of Homeomorphisms on Homogeneous Spaces of a Group Action

2023/08/18 by Samuel A. Hokamp, Hokamp, Samuel A.
Mathematics · #Advanced Topology and Set Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2308.09799

Abstract

We develop a class of homeomorphisms on a compact homogeneous space of a transitive group action and show how the class sheds new light on a decomposition problem. We further use this class to show that every such homogeneous space in a locally convex topological vector space which is also convex must necessarily be trivial, ie. a singleton set. Additionally, this class of homeomorphisms allows us to relate the induced group action on the space of continuous functions to the action on the homogeneous space.

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