Classification of spaces of Continuous Function on ordinals

L. V. Genze; S. P. Gul'ko; T. E. Khmyleva

Classification of spaces of Continuous Function on ordinals

General Topology 2018-06-26 v1 Functional Analysis

Authors: L. V. Genze , S. P. Gul'ko , T. E. Khmyleva

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 $C_p([0,\alpha])$ 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

continuous function spaces ordinals topological classification pointwise convergence compact segments uniform classification

Cite

@article{arxiv.1806.09015,
  title  = {Classification of spaces of Continuous Function on ordinals},
  author = {L. V. Genze and S. P. Gul'ko and T. E. Khmyleva},
  journal= {arXiv preprint arXiv:1806.09015},
  year   = {2018}
}

Comments

7 pages; accepted by Commentationes Mathematicae Universitatis Carolinae

Classification of spaces of Continuous Function on ordinals

Abstract

Keywords

Cite

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