Classification of spaces of continuous functions on ordinals

Abstract

We conclude the classification of spaces of continuous functions on ordinals carried out by Górak [Górak R., {Function spaces on ordinals}, Comment. Math. Univ. Carolin. {46} (2005), no. 1, 93--103]. This gives a complete topological classification of the spaces $C_p([0,\alpha])$ of all continuous real-valued functions on compact segments of ordinals endowed with the topology of pointwise convergence. Moreover, this topological classification of the spaces $C_p([0,\alpha])$ completely coincides with their uniform classification.