Topological properties of the continuous function spaces on some ordered compacta

TL;DR

This paper investigates specific classes of compact spaces where the space of continuous functions exhibits a countable cover with small local norm diameters, revealing new topological properties of these function spaces.

Contribution

It introduces new classes of compacta for which the pointwise topology on continuous functions has a countable cover with small local norm diameters, advancing understanding of their topological structure.

Findings

Identification of new classes of compacta with specific topological properties.

Demonstration that $C(K)$ spaces on these compacta have countable covers with small local norm diameters.

Insights into the topological and functional structure of these spaces.

Abstract

Some new classes of compacta $K$ are considered for which $C(K)$ endowed with the pointwise topology has a countable cover by sets of small local norm--diameter.