Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
compact; countably compact; absolutely countably compact; hereditarily absolutely countably compact; topological group
compact; countably compact; absolutely countably compact; hereditarily absolutely countably compact; topological group
Summary:
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)].
References:
[1] Arhangel'skii A.V.: On bicompacta hereditarily satisfying Suslin's condition tightness and free sequences. Soviet Math. Dokl. 12 (1971), 1253-1257. MR 0119188
[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. MR 1485076 | Zbl 0937.54013
[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. MR 0776619
[4] Engelking R.: General Topology, Revised and completed edition. Heldermann Verlag Berlin (1989). MR 1039321
[5] Fleishman W.M.: A new extension of countable compactness. Fund. Math. 67 (1970), 1-9. MR 0264608
[6] Kombarov A.P.: On the product of normal spaces. Soviet. Math. Dokl. 13 (4) (1972), 1068-1071. Zbl 0259.54006
[7] Matveev M.V.: Absolutely countably compact spaces. Topology Appl. 58 (1994), 81-92. MR 1280711 | Zbl 0801.54021
[8] Matveev M.V.: A countably compact topological group which is not absolutely countably compact. Questions Answers Gen. Topology 11 (1993), 173-176. MR 1234212 | Zbl 0808.54025
[9] Stephenson R.M., Jr.: Initially $\kappa$-Compact and Related Space. Handbook of Set-theoertic Topology K. Kunen and J.E. Vaughan North-Holland Amsterdam (1984), 603-632. MR 0776632
[10] Vaughan J.E.: A countably compact, separable space which is not absolutely countably compact. Comment. Math. Univ. Carolinae 34 (1995), 197-200. MR 1334426 | Zbl 0833.54012
[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. MR 1460834 | Zbl 0917.54023
[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. MR 0776631 | Zbl 0562.54031
Search
Partner of
