Continuity up to a Covering and Connectedness

TL;DR

This paper explores a novel approach to understanding connectedness in topology by combining chain connectedness with continuity up to a covering, enabling the inheritance of connectedness without requiring continuous surjections.

Contribution

It introduces a new method that merges chain connectedness with continuity up to a covering to extend connectedness properties in topological spaces.

Findings

Connectedness can be inherited without continuous surjections.

The approach combines chain connectedness with continuity up to a covering.

New insights into topological space properties are provided.

Abstract

One of the ways that connectedness has been studied through the history of topology is by using chains, the so called chain connectedness. Here we combine this notion together with continuity up to a covering to provide the inheritance of connectedness for the topological spaces even when there is no continuous surjection between them.