On Topological Groups of Monotonic Autohomeomorphisms

TL;DR

This paper investigates conditions under which the set of monotonic autohomeomorphisms on a generalized ordered space forms a topological group, focusing on the interplay between order properties and topological structure.

Contribution

It establishes a necessary and sufficient condition for the set of monotonic autohomeomorphisms to constitute a topological group with point-wise convergence topology.

Findings

Identifies a key condition for topological group structure

Characterizes the topology of monotonic autohomeomorphisms

Provides insights into ordered space automorphisms

Abstract

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