Classification of spaces of Continuous Function on ordinals

2018/06/23 by L. V. Genze, Genze, L. V., S. P. Gul'ko +3
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.1806.09015

openalex publication_date 2018/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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,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.

Related

• Complete topological classification of Baire spaces functions on ordinals
• The uniform convergence topology on separable subsets
• Topological properties of function spaces over ordinals
• Function spaces on separable compact lines
• About the space of continuous functions with open domain