Uniform limits of $\mathcal B_1^{**}$-functions

TL;DR

This paper characterizes the uniform limits of functions from Pawlak's class _1^{**}, exploring their properties and connections with their linear span within a topological space framework.

Contribution

It introduces the class uS_1 as the uniform limits of _1^{**} functions and analyzes its structure and relation to oscillation rank one functions.

Findings

uS_1 contains functions with oscillation rank one.

The class uS_1 is connected to its linear span.

The study uses a general topological space setting.

Abstract

We characterise the class of uniform limits of functions from Pawlak's class $\mathcal B_1^{**}$. The resulting class $u\mathscr S_1$, which contains functions with the oscillation rank one, is discussed in connection with its linear span. We apply a general, topological space, setting in our discussion.