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

Abstract

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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 , 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.

How to cite

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Genze, 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 -

References

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  5. Górak R., Function spaces on ordinals, Comment. Math. Univ. Carolin. 46 (2005), no. 1, 93–103. MR2175862
  6. Gul'ko S. P., Free topological groups and a space of continuous functions on ordinals, Vestnik of Tomsk State University (2003), no. 280, 34–38 (Russian). 
  7. Gul'ko S. P., Os'kin A. V., Isomorphic classification of spaces of continuous functions on totally ordered compact sets, Funkcional Anal. i Priložen. 9 (1975) no. 1, 56–57 (Russian). MR0427401
  8. Kislyakov S. V., 10.1007/BF00967506, Siberian Math. J. 16 (1975), no. 2, 226–231; translated from Sibirskii Matematicheskij Zhurnal 16 (1975), no. 2, 293–300 (Russian). MR0377490DOI10.1007/BF00967506
  9. Semadeni Z., Banach spaces non-isomorphic to their Cartesian squares. II, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 8 (1960), 81–84. MR0115074
  10. Tkachuk V. V., A C p -Theory Problem Book, Topological and Function Spaces, Problem Books in Mathematics, Springer, New York, 2011. MR3024898

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