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