Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
compact; countably compact; absolutely countably compact; hereditarily absolutely countably compact; $\omega $-bounded; countable tightness; sequential space
compact; countably compact; absolutely countably compact; hereditarily absolutely countably compact; $\omega $-bounded; countable tightness; sequential space
Summary:
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.
References:
[Arh] Arhangel'skii A.V.: On bicompacta hereditarily satisfying the Souslin condition. Tightness and free sequences. Soviet Math. Dokl. 12 (1971), 1253-1257.
[Bal] Balogh Z.: On compact space of countable tightness. Proc. Amer. Math. Soc. 105 (1989), 756-764. MR 0930252
[Bon] Bonanzinga M.: Preservation and reflection of properties acc and hacc. Comment. Math. Univ. Carolinae 37,1 (1996), 147-153. MR 1396166 | Zbl 0917.54027
[vD] 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. MR 0776619 | Zbl 0561.54004
[Eng] Engelking R.: General Topology. Warszawa (1977). MR 0500780 | Zbl 0373.54002
[FL] Fletcher P., Lindgren W.F.: Quasi-uniform spaces. Marcel Dekker, New York, 1982. MR 0660063 | Zbl 0583.54017
[GFW] Gulden S.L., Fleischman W.F., Weston J.H.: Linearly ordered topological spaces. Proc. Amer. Math. Soc. 24 (1970), 197-203. MR 0250272 | Zbl 0203.55104
[Mal] Malyhin V.I.: On the tightness and the Suslin number of $exp X$ and of a product of spaces. Soviet Math. Dokl. 13 (1972), 496-499.
[Mat1] Matveev M.V.: Absolutely countably compact spaces. Topology and Appl. 58 (1994), 81-92. MR 1280711 | Zbl 0801.54021
[Mat2] Matveev M.V.: A countably compact topological group which is not absolutely countably compact. Questions and Answers 11 (1993), 173-176. MR 1234212 | Zbl 0808.54025
[Vau1] 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. MR 1078647
[Vau2] 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. MR 1460834
Search
Partner of
