Topological properties of $q$-analogues of multiple zeta values

TL;DR

This paper investigates the topological characteristics of $q$-analogues of multiple zeta values, focusing on their convergence properties and the structure of their derived sets within a function space.

Contribution

It provides new insights into the topological behavior and derived set structures of $q$-analogues of multiple zeta values, a topic not extensively explored before.

Findings

Identified the convergence behavior of certain $q$-analogues of multiple zeta values.

Determined the derived sets of specific $q$-analogue sets.

Analyzed the topological structure of these $q$-analogues in function spaces.

Abstract

In the space of bounded real-valued functions on the interval $(0,1)$, we study the convergent sequences of $q$-analogues of multiple zeta values which do not converge to $0$. And we obtain the derived sets of the set of some $q$-analogue of multiple zeta values.