On continuous functions on two-dimensional disk which are regular in its interior points

TL;DR

This paper introduces a class of regular continuous functions on the closed 2-disk and demonstrates that each function in this class is topologically conjugate to a linear function on a simple geometric domain.

Contribution

The paper characterizes a new class of regular continuous functions on the 2-disk and establishes their topological conjugacy to linear functions on basic geometric shapes.

Findings

Functions are topologically conjugate to linear functions on simple domains

The class of functions is well-defined and includes interior-regular functions

Provides a topological classification of these functions

Abstract

We introduce a class of regular continuous functions on the closed 2-disk and show that each function from this class is topologically conjugate to a linear function defined on a sqare, a closed half-disk or a closed disk.