Classification of spaces of Continuous Function on ordinals

L. V. Genze, S. P. Gul'ko, T. E. Khmyleva

Published 2018-06-23Version 1

We conclude the classification of spaces of continuous functions on ordinals carried out by R. Gorak. 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.