Sequential topological groups of any sequential order under CH

Alexander Shibakov

Fundamenta Mathematicae (1998)

  • Volume: 155, Issue: 1, page 79-89
  • ISSN: 0016-2736

Abstract

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For any α < ω 1 a countable sequential topological group of sequential order α is constructed using CH.

How to cite

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Shibakov, Alexander. "Sequential topological groups of any sequential order under CH." Fundamenta Mathematicae 155.1 (1998): 79-89. <http://eudml.org/doc/212244>.

@article{Shibakov1998,
abstract = {For any $α < ω_1$ a countable sequential topological group of sequential order α is constructed using CH.},
author = {Shibakov, Alexander},
journal = {Fundamenta Mathematicae},
keywords = {sequential space; sequential order; topological group},
language = {eng},
number = {1},
pages = {79-89},
title = {Sequential topological groups of any sequential order under CH},
url = {http://eudml.org/doc/212244},
volume = {155},
year = {1998},
}

TY - JOUR
AU - Shibakov, Alexander
TI - Sequential topological groups of any sequential order under CH
JO - Fundamenta Mathematicae
PY - 1998
VL - 155
IS - 1
SP - 79
EP - 89
AB - For any $α < ω_1$ a countable sequential topological group of sequential order α is constructed using CH.
LA - eng
KW - sequential space; sequential order; topological group
UR - http://eudml.org/doc/212244
ER -

References

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  1. [DP] S. Dolecki and R. Peirone, Topological semigroups of every countable sequential order, in: Recent Developments of General Topology and its Applications, Akademie-Verlag, 1992, 80-84. Zbl0799.22002
  2. [F] L. Foged, Sequential order of homogeneous and product spaces, Topology Proc. 6 (1981), 287-298. Zbl0517.54021
  3. [M] E. Michael, A quintuple quotient quest, Gen. Topology Appl. 2 (1972), 91-138. Zbl0238.54009
  4. [N] P. J. Nyikos, Metrizability and Fréchet-Urysohn property in topological groups, Proc. Amer. Math. Soc. 83 (1981), 793-801. Zbl0474.22001
  5. [P] R. Peirone, Regular semitopological groups of every countable sequential order, Topology Appl. 58 (1994), 145-149. Zbl0837.54022
  6. [S1] A. Shibakov, Sequential group topology on rationals with intermediate sequential order, Proc. Amer. Math. Soc. 124 (1996), 2599-2607. Zbl0865.54022
  7. [S2] A. Shibakov, Metrizability of sequential topological groups with point-countable k-networks, Proc. Amer. Math. Soc., to appear. Zbl0903.54016

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