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Automatic continuity for vector spaces with linear topology

Samuel Quirino, Lucas H. R. de Souza

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.

Automatic continuity for vector spaces with linear topology

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.
Paper Structure (6 sections, 29 theorems, 3 equations)

This paper contains 6 sections, 29 theorems, 3 equations.

Table of Contents

  1. Preliminaries
  2. Linear algebra and cardinals
  3. Vector spaces with linear topology
  4. Codimension topology
  5. Some properties of vector spaces with codimension topology
  6. Some remarks about algebras

Key Result

Proposition 1.1

Let $V$ be a vector space, $W,W' < V$ and $\kappa$ a cardinal number satisfying $\kappa = 1$ or $\kappa \geqslant \aleph_{0}$. If $codim \ W < \kappa$ and $codim \ W' < \kappa$, then $codim \ W \cap W' < \kappa$.

Theorems & Definitions (72)

  • Proposition 1.1
  • Remark 1.1
  • proof
  • Proposition 1.2
  • proof
  • Proposition 1.3
  • Definition 1.4
  • Definition 1.5
  • Proposition 1.6
  • Remark 1.2
  • ...and 62 more