Automatic continuity for vector spaces with linear topology

TL;DR

This paper classifies topological vector spaces with linear topology where all algebraic automorphisms are continuous, providing a comprehensive understanding of their structure and properties.

Contribution

It offers a complete classification of such spaces and explores their key properties, advancing the theory of topological vector spaces.

Findings

Classification of all topological vector spaces with this automorphism property

Identification of key properties of these spaces

Insights into the structure of automorphisms in linear topologies

Abstract

In this paper we classify all topological vector spaces with linear topology with the property that all algebraic automorphisms are continuous. Moreover, we prove some properties of these spaces.