Functionally $\sigma$-discrete mappings and a generalization of Banach's theorem

TL;DR

This paper introduces a new class of mappings called $\sigma$-strongly functionally discrete mappings, expanding existing classes and generalizing Banach's theorem on analytically representable functions.

Contribution

It defines $\sigma$-strongly functionally discrete mappings and extends Banach's theorem to this broader class.

Findings

Introduces $\sigma$-strongly functionally discrete mappings

Generalizes Banach's theorem for these mappings

Expands the class of $\sigma$-discrete mappings

Abstract

We present $\sigma$-strongly functionally discrete mappings which expand the class of $\sigma$-discrete mappings and generalize Banach's theorem on analytically representable functions