Any countable topological $\mathbb F_p$-vector space has a closed discrete basis

TL;DR

The paper proves that all countable topological vector spaces over finite fields have a closed discrete basis, linking topological vector spaces and Abelian groups of prime exponent.

Contribution

It establishes that every countable topological vector space over a finite field possesses a closed discrete basis, a novel structural insight.

Findings

Any countable topological vector space over $\\mathbb{F}_p$ has a closed discrete basis.

Equivalent to countable Abelian topological groups of prime exponent having such a basis.

Provides a new understanding of the structure of these spaces.

Abstract

It is proved that any countable topological vector space over a finite field $\mathbb F_p$ or, equivalently, any countable Abelian topological group of prime exponent has a closed discrete basis.