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arXiv · 2308.09799

A Class of Homeomorphisms on Homogeneous Spaces of a Group Action

Samuel A. Hokamp
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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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Samuel A. Hokamp. 2023-08-18. A Class of Homeomorphisms on Homogeneous Spaces of a Group Action. https://arxiv.org/abs/2308.09799

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