Absolute countable compactness of products and topological groups

Yan-Kui Song

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 2, page 367-372
  • ISSN: 0010-2628

Abstract

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In this paper, we generalize Vaughan's and Bonanzinga's results on absolute countable compactness of product spaces and give an example of a separable, countably compact, topological group which is not absolutely countably compact. The example answers questions of Matveev [8, Question 1] and Vaughan [9, Question (1)].

How to cite

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Song, Yan-Kui. "Absolute countable compactness of products and topological groups." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 367-372. <http://eudml.org/doc/248415>.

@article{Song1999,
abstract = {In this paper, we generalize Vaughan's and Bonanzinga's results on absolute countable compactness of product spaces and give an example of a separable, countably compact, topological group which is not absolutely countably compact. The example answers questions of Matveev [8, Question 1] and Vaughan [9, Question (1)].},
author = {Song, Yan-Kui},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {compact; countably compact; absolutely countably compact; hereditarily absolutely countably compact; topological group; absolutely countably compact spaces; topological group},
language = {eng},
number = {2},
pages = {367-372},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Absolute countable compactness of products and topological groups},
url = {http://eudml.org/doc/248415},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Song, Yan-Kui
TI - Absolute countable compactness of products and topological groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 2
SP - 367
EP - 372
AB - In this paper, we generalize Vaughan's and Bonanzinga's results on absolute countable compactness of product spaces and give an example of a separable, countably compact, topological group which is not absolutely countably compact. The example answers questions of Matveev [8, Question 1] and Vaughan [9, Question (1)].
LA - eng
KW - compact; countably compact; absolutely countably compact; hereditarily absolutely countably compact; topological group; absolutely countably compact spaces; topological group
UR - http://eudml.org/doc/248415
ER -

References

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  1. Arhangel'skii A.V., On bicompacta hereditarily satisfying Suslin's condition tightness and free sequences, Soviet Math. Dokl. 12 (1971), 1253-1257. (1971) MR0119188
  2. Bonanzinga M., On the product of a compact space with an hereditarily absolutely countably compact space, Comment. Math. Univ. Carolinae 38 (1997), 557-562. (1997) Zbl0937.54013MR1485076
  3. van Douwen E.K., The Integer and Topology, Handbook of Set-theoertic Topology K. Kunen and J.E. Vaughan North-Holland Amsterdam (1984), 111-167. (1984) MR0776619
  4. Engelking R., General Topology, Revised and completed edition, Heldermann Verlag Berlin (1989). (1989) MR1039321
  5. Fleishman W.M., A new extension of countable compactness, Fund. Math. 67 (1970), 1-9. (1970) MR0264608
  6. Kombarov A.P., On the product of normal spaces, Soviet. Math. Dokl. 13 (4) (1972), 1068-1071. (1972) Zbl0259.54006
  7. Matveev M.V., Absolutely countably compact spaces, Topology Appl. 58 (1994), 81-92. (1994) Zbl0801.54021MR1280711
  8. Matveev M.V., A countably compact topological group which is not absolutely countably compact, Questions Answers Gen. Topology 11 (1993), 173-176. (1993) Zbl0808.54025MR1234212
  9. Stephenson R.M., Jr., Initially κ -Compact and Related Space, Handbook of Set-theoertic Topology K. Kunen and J.E. Vaughan North-Holland Amsterdam (1984), 603-632. (1984) MR0776632
  10. Vaughan J.E., A countably compact, separable space which is not absolutely countably compact, Comment. Math. Univ. Carolinae 34 (1995), 197-200. (1995) Zbl0833.54012MR1334426
  11. Vaughan J.E., On the product of a compact space with an absolutely countably compact space, Annals of New York Acad. Soc. 788 (1996), 203-208. (1996) Zbl0917.54023MR1460834
  12. Vaughan J.E., Countably Compact and Sequentially Compact Spaces, Handbook of Set-theoertic Topology K. Kunen and J.E. Vaughan North-Holland Amsterdam (1984), 569-602. (1984) Zbl0562.54031MR0776631

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