The existence of LUR-norms on spaces of continuous functions on Fedorchuk compacta

TL;DR

This paper constructs a locally uniformly rotund (LUR) norm on the space of continuous functions over Fedorchuk compacta of height 3, which is lower semicontinuous in the pointwise topology, advancing the understanding of geometric structures in function spaces.

Contribution

It introduces a new LUR-norm on C(K) spaces for Fedorchuk compacta of height 3, demonstrating specific geometric properties of these function spaces.

Findings

Established an LUR-norm on C(K) for Fedorchuk compacta of height 3.

Proved the norm is lower semicontinuous in the pointwise topology.

Extended the class of spaces with known LUR-norms.

Abstract

We construct an LUR-norm on the space C(K) which is lower semicontinuous with respect to the pointwise topology for any Fedorchuk compactum of height 3.