## Leonid V. Genze, Sergei P. Gul'ko, Tat'ana E. Khmyleva

*Classification of spaces of continuous functions on ordinals*

Comment.Math.Univ.Carolin. 59,3 (2018) 365-370.**Abstract:**We conclude the classification of spaces of continuous functions on ordinals carried out by G\'orak [G\'orak R., {\it Function spaces on ordinals}, Comment.\ Math.\ Univ.\ Carolin.\ {\bf 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.

**Keywords:** space of continuous functions; pointwise topology; homeomorphism of function spaces; uniform homeomorphism; ordinal number

**DOI:** DOI 10.14712/1213-7243.2015.250

**AMS Subject Classification:** 54C35

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