DOI QR코드

DOI QR Code

ISOCOMPACTNESS AND RELATED TOPICS OF WEAK COVERING PROPERTY

  • Published : 2002.05.01

Abstract

In this paper, we study the concepts of isocompactness and cl-isocompactness. We generalize a pure space defined by Arhangelskii and get some results on initially K-compact spaces. We also consider open problems related to isocompactness and cl-isocompactness.

Keywords

References

  1. A. V. Arhangel'skii, The star method, new classes of spaces and countable compactness, Soviet Math. Dokl. 21 (1980), 550-554.
  2. P. Bacon, The compactness of countably compact spaces, Pacific J. Math. 32 (1970), 587-592. https://doi.org/10.2140/pjm.1970.32.587
  3. R. L. Blair, Closed-completeness in spaces with weak covering properties, Settheoretic Topology, Academic Press, New York-San Francisco-London, 1977, pp. 17-45.
  4. R. L. Blair, On a theorem of Chaber Topology Proceedings 5 (1980), 33-46.
  5. D. K. Burke, Covering Properties, in Handbook of Set-theoretic Topology, North-Holland, Amsterdam, 1984, pp. 349-422.
  6. J. Cao, On isocompactness of function spaces, Bull. Austral. Math. Soc. 60 (1999), 483-486. https://doi.org/10.1017/S0004972700036649
  7. J. Chaber, Conditions which imply compactness in countably compact spaces, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 24 (1976), 993-998.
  8. M. H. Cho, Isocompactness of weakly star reducible spaces, Q & A in General Topology 14 (1996), 123-129.
  9. S. W. Davis, A cushioning-type weak covering property, Pacific J. Math. 80 (1979), 359-370. https://doi.org/10.2140/pjm.1979.80.359
  10. S. W. Davis, On F${\tau}$-spaces, General Topology and Appl. 9 (1978), 131-138. https://doi.org/10.1016/0016-660X(78)90058-2
  11. J. Dugundji, Topology, Allyn and Bacon, 1966.
  12. N. Dykes, Generalizations of realcompact spaces, Pacific J. Math. 33 (1970), 571-581. https://doi.org/10.2140/pjm.1970.33.571
  13. F. W. Eckertson, S. Garcia-Ferreira, M. Sanchis, and S. Watson, An isocompact Tychonoff space whose square is not isocompact, Topology Proceedings 22 (1997),181-190.
  14. R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.
  15. S. Garcia-Ferreira and M. Sanchis, Projection maps and isocompactness (preprint).
  16. L. Gillman and M. Jerison, Rings of continuous functions, Princeton, 1960.
  17. J. D. Hansard, Function space topologies, Pacific J. Math. 35 (1970), 381-388. https://doi.org/10.2140/pjm.1970.35.381
  18. E. Hewitt, Rings of real continuous functions, Trans. Amer. Math. Soc. 64 (1948), 49-99. https://doi.org/10.1090/S0002-9947-1948-0026239-9
  19. M. Ismail and P. J. Nyikos, On spaces in which countably compact sets are closed, and hereditary properties, Top. Appl. 11 (1980), 281-292. https://doi.org/10.1016/0166-8641(80)90027-9
  20. M. Ismail and A. Szymanski, Compact spaces representable as unions of nice subspaces, Topology and its Appl. 59 (1994), 287-298. https://doi.org/10.1016/0166-8641(94)90025-6
  21. I. Juhasz, K. Kunen, and M. E. Rudin, Two more hereditarily separable non-Lindelöf space, Canad. J. Math. 28 (1976), 998-1005. https://doi.org/10.4153/CJM-1976-098-8
  22. M. V. Matveev, A survey on star covering properties, Topology Atlas Preprint #330, 1998.
  23. R. L. Moore, Foundations of point set theory, rev. ed., Amer. Math. Soc. Colloq. Publ. 13, Amer. Math. Soc. Providence, R.I., 1962.
  24. S. Nedev, Symmetrizable spaces and final compactness, Soviet Math. Dokl. 8 (1967), 890-892.
  25. G. M. Reed, The intersection topology with respect to the real line and the countable ordinals, Trans. Amer. Math. Soc. 297 (1986), 509-520. https://doi.org/10.2307/2000536
  26. M. Sakai, On CL-isocompactness and weak Borel completeness, Tsukuba J. Math. 8 (1984), 377-382. https://doi.org/10.21099/tkbjm/1496160049
  27. M. Sakai, A new class of isocompact spaces and related results, Pacific J. Math. 122 (1986), 211-22l. https://doi.org/10.2140/pjm.1986.122.211
  28. R. M. Stephenson Jr., Initially K-compact and related spaces, in Handbook of Set-theoretic Topology, North-Holland, Amsterdam, 1984, pp. 603-632.
  29. J. E. Vaughan, Countably compact and sequentially compact spaces, in Handbook of Set-theoretic Topology, North-Holland, Amsterdam, 1984, pp. 569-602.
  30. J. M. Worrell, Jr and H. H. Wicke, A covering property which implies isocompactness I, Proc. Amer. Math. Soc. 79 (1979), 331-334. https://doi.org/10.1090/S0002-9939-1980-0565365-6
  31. H. H. Wicke and J. M. Worrell, Jr, A covering property which implies isocompactness II, Topology Proceedings 4 (1979), 213-224.
  32. H. H. Wicke and J. M. Worrell, Jr, Characterizations of paracompactness and subparacompactness using star reducibility, Proc. Amer. Math. Soc. 111 (1991), 1119-1127. https://doi.org/10.1090/S0002-9939-1991-1054164-4
  33. H. H. Wicke, Not all realcompact spaces are ultrapure, Topology and its Appl. 91 (1999), 87-90. https://doi.org/10.1016/S0166-8641(97)00246-0