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On the weight of a topological space


Author: R. E. Hodel
Journal: Proc. Amer. Math. Soc. 43 (1974), 470-474
MSC: Primary 54A25
DOI: https://doi.org/10.1090/S0002-9939-1974-0334125-0
MathSciNet review: 0334125
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Abstract: The main result in this paper states that the weight of a regular space is the product of three cardinal functions, namely the Lindelöf degree, the pluming degree, and the point separating weight.


References [Enhancements On Off] (What's this?)

  • [1] G. Aquaro, Point-countable open coverings in countably compact spaces, General Topology and its Relations to Modern Analysis and Algebra. II, Academia, Prague, 1966, pp. 39-41.
  • [2] A. V. Arhangel'skiĭ, Bicompact sets and the topology of spaces, Trudy Moskov. Mat. Obšč. 13 (1965), 3-55 = Trans. Moscow Math. Soc. 1965, 1-62. MR 33 #3251. MR 0195046 (33:3251)
  • [3] -, On the cardinality of bicompacta satisfying the first axiom of countability, Dokl. Akad. Nauk SSSR 187 (1969), 967-970 = Soviet Math. Dokl. 10 (1969), 951-955. MR 40 #4922. MR 0251695 (40:4922)
  • [4] -, On a class of spaces containing all metric and all locally bicompact spaces, Mat. Sb. 67 (109) (1965), 55-88; English transl., Amer. Math. Soc. Transl. (2) 92 (1970), 1-39. MR 32 #8299; 42 #3. MR 0190889 (32:8299)
  • [5] D. K. Burke, On $ p$-spaces and $ w\Delta $-spaces, Pacific J. Math. 35 (1970), 285-296. MR 43 #3986. MR 0278255 (43:3986)
  • [6] W. W. Comfort, A survey of cardinal invariants, General Topology and Appl. 1 (1971), no. 2, 163-199. MR 44 #7510. MR 0290326 (44:7510)
  • [7] V. V. Filippov, On feathered paracompacta, Dokl. Akad. Nauk SSSR 178 (1968), 555-558 = Soviet Math. Dokl. 9 (1968), 161-164. MR 37 #3519. MR 0227935 (37:3519)
  • [8] W. Holsztyński, Hausdorff spaces of minimal weight, Dokl. Akad. Nauk SSSR 168 (1966), 508-509 = Soviet Math. Dokl. 7 (1966), 667-668. MR 33 #3242. MR 0195037 (33:3242)
  • [9] I. Juhász, Cardinal functions in topology, Mathematical Centre, Amsterdam, 1971.
  • [10] E. Michael, A note on closed maps and compact sets, Israel J. Math. 2 (1964), 173-176. MR 31 #1659. MR 0177396 (31:1659)
  • [11] A. S. Miščenko, Spaces with point-countable bases, Dokl. Akad. Nauk SSSR 144 (1962), 985-988 = Soviet Math. Dokl. 3 (1962), 855-858. MR 25 #1537. MR 0138090 (25:1537)
  • [12] J. Nagata, A note on Filippov's theorem, Proc. Japan Acad. 45 (1969), 30-33. MR 39 #7557. MR 0246253 (39:7557)
  • [13] V. I. Ponomarev, Metrizability of a finally compact $ p$-space with a point-countable base, Dokl. Akad. Nauk SSSR 174 (1967), 1274-1277 = Soviet Math. Dokl. 8 (1967), 765-768. MR 35 #7298. MR 0216465 (35:7298)
  • [14] H. H. Wicke and J. M. Worrell, Jr., Characterizations of developable spaces, Canad. J. Math. 17 (1965), 820-830. MR 32 #427. MR 0182945 (32:427)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0334125-0
Keywords: Weight, Lindelöf degree, $ p$-space, separating open cover
Article copyright: © Copyright 1974 American Mathematical Society

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