Indicator sequences and indicator topologies of Fort transformation groups

TL;DR

This paper characterizes the possible indicator sequences and topologies of Fort transformation groups, establishing conditions for their existence and extending the study to semigroups.

Contribution

It provides a complete characterization of indicator sequences and topologies for Fort transformation groups and semigroups, including existence conditions.

Findings

Existence of Fort transformation groups with given indicator sequences characterized.

All possible indicator topological spaces for Fort transformation groups described.

Extension of study to Fort transformation semigroups included.

Abstract

In the following text we prove that there exists a Fort transformation group with indicator sequence $(p_0,\ldots,p_n)$ if and only if $0=p_0\leq p_1\leq\cdots\leq p_n=1$, moreover we characterize all possible indicator topological spaces of Fort transformation groups.The text will study indicator sequences and indicator topologies of Fort transformation semigroups too.