On the product of a compact space with an hereditarily absolutely countably compact space

Maddalena Bonanzinga

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 3, page 557-562
  • ISSN: 0010-2628

Abstract

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We show that the product of a compact, sequential T 2 space with an hereditarily absolutely countably compact T 3 space is hereditarily absolutely countably compact, and further that the product of a compact T 2 space of countable tightness with an hereditarily absolutely countably compact ω -bounded T 3 space is hereditarily absolutely countably compact.

How to cite

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Bonanzinga, Maddalena. "On the product of a compact space with an hereditarily absolutely countably compact space." Commentationes Mathematicae Universitatis Carolinae 38.3 (1997): 557-562. <http://eudml.org/doc/248108>.

@article{Bonanzinga1997,
abstract = {We show that the product of a compact, sequential $T_2$ space with an hereditarily absolutely countably compact $T_3$ space is hereditarily absolutely countably compact, and further that the product of a compact $T_2$ space of countable tightness with an hereditarily absolutely countably compact $\omega $-bounded $T_3$ space is hereditarily absolutely countably compact.},
author = {Bonanzinga, Maddalena},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {compact; countably compact; absolutely countably compact; hereditarily absolutely countably compact; $\omega $-bounded; countable tightness; sequential space; absolutely countably compact space; cartesian product},
language = {eng},
number = {3},
pages = {557-562},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the product of a compact space with an hereditarily absolutely countably compact space},
url = {http://eudml.org/doc/248108},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Bonanzinga, Maddalena
TI - On the product of a compact space with an hereditarily absolutely countably compact space
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 3
SP - 557
EP - 562
AB - We show that the product of a compact, sequential $T_2$ space with an hereditarily absolutely countably compact $T_3$ space is hereditarily absolutely countably compact, and further that the product of a compact $T_2$ space of countable tightness with an hereditarily absolutely countably compact $\omega $-bounded $T_3$ space is hereditarily absolutely countably compact.
LA - eng
KW - compact; countably compact; absolutely countably compact; hereditarily absolutely countably compact; $\omega $-bounded; countable tightness; sequential space; absolutely countably compact space; cartesian product
UR - http://eudml.org/doc/248108
ER -

References

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  1. Arhangel'skii A.V., On bicompacta hereditarily satisfying the Souslin condition. Tightness and free sequences, Soviet Math. Dokl. 12 (1971), 1253-1257. (1971) 
  2. Balogh Z., On compact space of countable tightness, Proc. Amer. Math. Soc. 105 (1989), 756-764. (1989) MR0930252
  3. Bonanzinga M., Preservation and reflection of properties acc and hacc, Comment. Math. Univ. Carolinae 37,1 (1996), 147-153. (1996) Zbl0917.54027MR1396166
  4. van Douwen E.K., The integers and topology, Handbook Set-theoretic Topology, K. Kunen and J.E. Vaughan Eds., Elsevier Sci. Publ. (1984), 111-167. (1984) Zbl0561.54004MR0776619
  5. Engelking R., General Topology, Warszawa (1977). (1977) Zbl0373.54002MR0500780
  6. Fletcher P., Lindgren W.F., Quasi-uniform spaces, Marcel Dekker, New York, 1982. Zbl0583.54017MR0660063
  7. Gulden S.L., Fleischman W.F., Weston J.H., Linearly ordered topological spaces, Proc. Amer. Math. Soc. 24 (1970), 197-203. (1970) Zbl0203.55104MR0250272
  8. Malyhin V.I., On the tightness and the Suslin number of e x p X and of a product of spaces, Soviet Math. Dokl. 13 (1972), 496-499. (1972) 
  9. Matveev M.V., Absolutely countably compact spaces, Topology and Appl. 58 (1994), 81-92. (1994) Zbl0801.54021MR1280711
  10. Matveev M.V., A countably compact topological group which is not absolutely countably compact, Questions and Answers 11 (1993), 173-176. (1993) Zbl0808.54025MR1234212
  11. Vaughan J.E., Small uncountable cardinals and topology, Open Problems in Topology, J. van Mill, G.M. Reed Eds., North-Holland, Amsterdam (1990), 195-218. (1990) MR1078647
  12. Vaughan J.E., On the product of a compact space with an absolutely compact space, Papers on General Topology and Applications, Annals of the New York Academy of Sciences 788 (1996), 203-208. (1996) MR1460834

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