Generalization of a Real-Analysis Result to a Class of Topological Vector Spaces

TL;DR

This paper extends a fundamental real-analysis theorem to a broader class of topological vector spaces and provides a counterexample where the generalization does not hold.

Contribution

It introduces a generalization of a classical real-analysis result to topological vector spaces and identifies limitations through a specific counterexample.

Findings

The theorem is successfully generalized to certain topological vector spaces.

A specific example shows the limits of this generalization.

The paper clarifies conditions under which the result applies.

Abstract

In this paper, we generalize an elementary real-analysis result to a class of topological vector spaces. We also give an example of a topological vector space to which the result cannot be generalized.