# Urysohn Lemmas in Topological Vector Spaces

## TL;DR

This paper extends the classical Urysohn lemma to topological vector spaces, introducing two variants with quasi-convex continuous functions, broadening the lemma's applicability.

## Contribution

It presents two new versions of the Urysohn lemma tailored for topological vector spaces with quasi-convex functions, a novel extension of classical results.

## Key findings

- Two variants of Urysohn lemma for topological vector spaces.
- Construction of quasi-convex continuous functions in these lemmas.
- Extension of classical Urysohn lemma to a broader context.

## Abstract

Two variations of classical Urysohn lemma for subsets of topological vector spaces are obtained in this article. The continuous functions constructed in these lemmas are of quasi-convex type.