# Classification of spaces of continuous functions on ordinals

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

Commentationes Mathematicae Universitatis Carolinae (2018)

- Volume: 59, Issue: 3, page 365-370
- ISSN: 0010-2628

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topGenze, Leonid V., Gul'ko, Sergei P., and Khmyleva, Tat'ana E.. "Classification of spaces of continuous functions on ordinals." Commentationes Mathematicae Universitatis Carolinae 59.3 (2018): 365-370. <http://eudml.org/doc/294164>.

@article{Genze2018,

abstract = {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.},

author = {Genze, Leonid V., Gul'ko, Sergei P., Khmyleva, Tat'ana E.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {space of continuous functions; pointwise topology; homeomorphism of function spaces; uniform homeomorphism; ordinal number},

language = {eng},

number = {3},

pages = {365-370},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Classification of spaces of continuous functions on ordinals},

url = {http://eudml.org/doc/294164},

volume = {59},

year = {2018},

}

TY - JOUR

AU - Genze, Leonid V.

AU - Gul'ko, Sergei P.

AU - Khmyleva, Tat'ana E.

TI - Classification of spaces of continuous functions on ordinals

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2018

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 59

IS - 3

SP - 365

EP - 370

AB - 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.

LA - eng

KW - space of continuous functions; pointwise topology; homeomorphism of function spaces; uniform homeomorphism; ordinal number

UR - http://eudml.org/doc/294164

ER -

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