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A characterization of primitive bases


Authors: H. H. Wicke and J. M. Worrell
Journal: Proc. Amer. Math. Soc. 50 (1975), 443-450
MSC: Primary 54E99
DOI: https://doi.org/10.1090/S0002-9939-1975-0425922-2
MathSciNet review: 0425922
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Abstract: The concept of primitive base is characterized in terms of primitive sequences. A characterization of essentially $ {T_1}$ spaces having bases of countable order is a corollary.


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  • [1] H. R. Bennett, On quasi-developable spaces, General Topology and Appl. 1 (1971), 253-262. MR 44 #5921. MR 0288725 (44:5921)
  • [2] H. R. Bennett and D. J. Lutzer, A note on weak $ \theta $-refinability, General Topology and Appl. 2 (1972), 49-54. MR 46 #853. MR 0301697 (46:853)
  • [3] A. S. Davis, Indexed systems of neighborhoods for general topological spaces, Amer. Math. Monthly 68 (1961), 886-893. MR 35 #4869. MR 0214017 (35:4869)
  • [4] E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375-376. MR 27 #2956. MR 0152985 (27:2956)
  • [5] H. H. Wicke, Base of countable order theory and some generalizations, Proc. Univ. Houston Point Set Topology Conf. 1971, Houston, Tex., 1972. MR 0397667 (53:1525)
  • [6] H. H. Wicke and J. M. Worrell, Jr., Topological completeness of first countable Hausdorff spaces. I, Fund. Math. 75 (1972), 209-222. MR 46 #8189. MR 0309078 (46:8189)
  • [7] -, Pararegularity, Notices Amer. Math. Soc. 20 (1973), A-173. Abstract #701-54-15.
  • [8] -, Characterization of absolute sets of interior condensation, Notices Amer. Math. Soc. 20 (1973), A-401. Abstract #704-G6.
  • [9] -, The preservation of primitive base by certain open mappings, Notices Amer. Math. Soc. 20 (1973), A-533. Abstract #706-54-5.
  • [10] -, Uniformly primitively complete mappings, Notices Amer. Math. Soc. 20 (1973), A-675. Abstract #709-G23.
  • [11] J. M. Worrell, Jr. and H. H. Wicke, Concerning spaces having bases of countable order, Notices Amer. Math. Soc. 12 (1965), 343. Abstract #622-60.
  • [12] 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)
  • [13] -, A central metrization theorem. I, Notices Amer. Math. Soc. 20 (1973), A-355. Abstract #702-G2.
  • [14] J. M. Worrell, Jr. and H. H. Wicke, A central metrization theorem. II, Notices Amer. Math. Soc. 20 (1973), A-381. Abstract #703-G14.
  • [15] L. Zippin, On a problem of N. Aronszajn and an axiom of R. L. Moore, Bull. Amer. Math. Soc. 37 (1931), 276-280. MR 1562138

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0425922-2
Keywords: Primitive base, primitive sequence, $ \theta $-base, base of countable order, quasi-developable space, developable space, completeness
Article copyright: © Copyright 1975 American Mathematical Society

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