On topological groups of monotonic automorphisms

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.

Keywords

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