On linear topological spaces (linearly) homeomorphic to $R^\infty$

TL;DR

This paper proves that any infinite-dimensional locally convex linear topological space that is a direct limit of finite-dimensional metrizable compacta is linearly homeomorphic to the space R^infinity, establishing a broad classification result.

Contribution

It establishes a new classification theorem showing such spaces are linearly homeomorphic to R^infinity, extending understanding of infinite-dimensional topological vector spaces.

Findings

Spaces as direct limits of finite-dimensional compacta are homeomorphic to R^infinity

Provides a characterization of certain infinite-dimensional locally convex spaces

Extends the theory of infinite-dimensional topological vector spaces

Abstract

We prove that every infinite-dimensional (locally convex) linear topological space that can be expressed as a direct limit of finite-dimensional metrizable compacta is (linearly) homeomorphic to the space $R^\infty=\dlim R^n$.