On topological groups of monotonic automorphisms

Raushan Buzyakova

United States

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Accepted: 2023-12-14

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Published: 2024-04-02

DOI: https://doi.org/10.4995/agt.2024.18989
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Keywords:

linearly ordered topological space, generalized ordered topological space, topology of point-wise convergence, paratopological group, topological group, monotonic automorphism

Supporting agencies:

This research was not funded

Abstract:

We study topological groups of monotonic automorphisms on a generalized ordered space L. We find a condition that is necessary and sufficient for the set of all monotonic automorphism on L along with the function composition and the topology of point-wise convergence to be a topological group.

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References:

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D. J. Lutzer, On generalized ordered spaces, Dissertationes Mathematicae, Warszawa, 1970, pp. 33.

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B. V. Sorin, Compactifications of homeomorphism groups of linearly ordered compacta, Mathematical Notes 112 (2022), 126-141. https://doi.org/10.1134/S0001434622070148

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