Function spaces on ordinals

Rafał Górak

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 1, page 93-103
  • ISSN: 0010-2628

Abstract

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We give a partial classification of spaces C p ( [ 1 , α ] ) of continuous real valued functions on ordinals with the topology of pointwise convergence with respect to homeomorphisms and uniform homeomorphisms.

How to cite

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Górak, Rafał. "Function spaces on ordinals." Commentationes Mathematicae Universitatis Carolinae 46.1 (2005): 93-103. <http://eudml.org/doc/249518>.

@article{Górak2005,
abstract = {We give a partial classification of spaces $C_p([1,\alpha ])$ of continuous real valued functions on ordinals with the topology of pointwise convergence with respect to homeomorphisms and uniform homeomorphisms.},
author = {Górak, Rafał},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {function spaces; pointwise topology; uniform homeomorphisms; ordinal numbers; pointwise topology; uniform homeomorphisms; ordinal numbers},
language = {eng},
number = {1},
pages = {93-103},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Function spaces on ordinals},
url = {http://eudml.org/doc/249518},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Górak, Rafał
TI - Function spaces on ordinals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 1
SP - 93
EP - 103
AB - We give a partial classification of spaces $C_p([1,\alpha ])$ of continuous real valued functions on ordinals with the topology of pointwise convergence with respect to homeomorphisms and uniform homeomorphisms.
LA - eng
KW - function spaces; pointwise topology; uniform homeomorphisms; ordinal numbers; pointwise topology; uniform homeomorphisms; ordinal numbers
UR - http://eudml.org/doc/249518
ER -

References

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  1. Arkhangel'skii A.V., Topological Function Spaces, Kluwer Academic Publishers, Dordrecht, 1992. MR1144519
  2. Baars J., de Groot J., On topological and linear equivalence of certain function spaces, CWI Tract 86, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam, 1992. Zbl0755.54007MR1182148
  3. Gul'ko S.P., The space C p ( X ) for countable infinite compact X is uniformly homeomorphic to c 0 , Bull. Polish Acad. Sci. Math. 36 (1988), 391-396. (1988) MR1101684
  4. Gul'ko S.P., Spaces of continuous functions on ordinals and ultrafilters, Mat. Zametki 47 (1990), 26-34. (1990) MR1057084
  5. Kislyakov S.V., Classification of spaces of continuous functions of ordinals, Siberian Math. J. 16 (1975), 226-231. (1975) Zbl0327.46033

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