Geodesic
Classification of spaces of continuous functions on ordinals
Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 3, pp. 365-370.

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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.
DOI : 10.14712/1213-7243.2015.250
Classification : 54C35
Keywords: space of continuous functions; pointwise topology; homeomorphism of function spaces; uniform homeomorphism; ordinal number 
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Genze, Leonid V.; Gul'ko, Sergei P.; Khmyleva, Tat'ana E. Classification of spaces of continuous functions on ordinals. Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 3, pp. 365-370. doi : 10.14712/1213-7243.2015.250. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.250/

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