Function spaces over products with 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 $C_p(X\times {\tau }^{\prime })$ and $C_p(Y\times {\tau }^{\prime })$, where $\tau$ and ${\tau }^{\prime }$ are spaces of ordinals with some additional desired properties.