Function Spaces over Products with Ordinals

TL;DR

This paper investigates conditions under which homeomorphisms between certain function spaces over products with ordinal spaces imply similar homeomorphisms over other ordinal products, advancing understanding of their topological structure.

Contribution

It establishes criteria linking homeomorphisms of function spaces over products with different ordinal spaces, revealing new structural insights.

Findings

Homeomorphism implications between function spaces over ordinal products

Conditions for equivalence of function spaces with different ordinal factors

Enhanced understanding of topological properties of spaces involving ordinals

Abstract

We are concerned with the question of when a homeomorphism between $C_p(X\times \tau)$ and $C_p(Y\times \tau)$ implies the existence of a homeomorphism between $C_p(X\times \tau')$ and $C_p(Y\times \tau')$, where $\tau$ and $\tau'$ are spaces of ordinals with some additional desired properties.