Detecting topological groups which are (locally) homeomorphic to LF-spaces

TL;DR

This paper introduces a straightforward criterion for identifying topological groups that are (locally) homeomorphic to LF-spaces, aiding in the classification of such groups in topology.

Contribution

The paper provides a new, simple criterion for recognizing topological groups that are (locally) homeomorphic to LF-spaces, enhancing existing classification methods.

Findings

Criterion effectively distinguishes LF-space homeomorphic groups

Simplifies the recognition process for topological groups

Contributes to the classification theory of topological groups

Abstract

We present a simple-to-apply criterion for recognizing topological groups that are (locally) homeomorphic to LF-spaces.