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An example relating to Arhangelskiĭ's class $ {\rm MOBI}$


Author: James R. Boone
Journal: Proc. Amer. Math. Soc. 41 (1973), 615-618
MSC: Primary 54G20; Secondary 54D20
DOI: https://doi.org/10.1090/S0002-9939-1973-0328891-7
MathSciNet review: 0328891
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Abstract: A space in Arhangel'skiĭ's class MOBI is presented which fails to have two structural properties which are weaker than countable metacompactness. A space is countably metacompact if and only if it is countably $ \theta $-refinable and pointwise collectionwise normal for countable collections. This space does not have either of these properties.


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

  • [1] A. Arhangel'skiĭ, Mappings and spaces, Uspehi Mat. Nauk 21 (1966), no. 4 (130), 133-184=Russian Math. Surveys 21 (1966), no. 4, 115-162. MR 37 #3534. MR 0227950 (37:3534)
  • [2] H. R. Bennett, On Arhangel'skiĭ's class MOBI, Proc. Amer. Math. Soc. 26 (1970), 178-180. MR 42 #2425. MR 0267523 (42:2425)
  • [3] H. R. Bennett and E. S. Berney, Subparacompactness and $ {G_\delta }$-diagonals in Arhangel'skiĭ's class MOBI, Proc. Amer. Math. Soc. 30 (1971), 573-577. MR 44 #990. MR 0283760 (44:990)
  • [4] H. R. Bennett and D. J. Lutzer, A note on weak $ \theta $-refinability, General Topology and Appl. 2 (1972), 49-54. MR 0301697 (46:853)
  • [5] J. R. Boone, A characterization of metacompactness in the class of $ \theta $-refinable spaces, General Topology and Appl. 3 (1973). MR 0321004 (47:9537)
  • [6] J. Dugundji, Topology, Allyn and Bacon, Boston, Mass., 1966. MR 33 #1824. MR 0193606 (33:1824)
  • [7] S. Hanai, On open mappings. II, Proc. Japan Acad. 37 (1961), 233-238. MR 23 #A4116. MR 0126822 (23:A4116)
  • [8] R. E. Hodel, A note on subparacompact spaces, Proc. Amer. Math. Soc. 25 (1970), 842-845. MR 41 #7629. MR 0263024 (41:7629)
  • [9] H. H. Wicke and J. M. Worrell, Jr., Open continuous mappings of spaces having bases of countable order, Duke Math. J. 34 (1967), 255-271. MR 35 #979. MR 0210084 (35:979)
  • [10] J. M. Worrell, Jr. and H. H. Wicke, Characterizations of developable topological 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/S0002-9939-1973-0328891-7
Keywords: Arhangel'skiĭ's class MOBI, $ \theta $-refinable, pointwise collectionwise normal, countably metacompact
Article copyright: © Copyright 1973 American Mathematical Society

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