This is an announcement for the paper “Classification of spaces of Continuous Function on ordinals” by L. V. Genzehttps://arxiv.org/search/math?searchtype=author&query=Genze%2C+L+V, S. P. Gul'kohttps://arxiv.org/search/math?searchtype=author&query=Gul%27ko%2C+S+P, T. E. Khmylevahttps://arxiv.org/search/math?searchtype=author&query=Khmyleva%2C+T+E.
Abstract: 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.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1806.09015