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Classification of spaces of continuous functions on ordinals

Leonid V. Genze; Sergei P. Gul'ko; Tat'ana E. Khmyleva — 2018

Commentationes Mathematicae Universitatis Carolinae

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 $C_{p} ([0, α])$ 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 $C_{p} ([0, α])$ completely coincides with their uniform classification.

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