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Monotonically normal spaces. (English) Zbl 0269.54009


MSC:

54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54E20 Stratifiable spaces, cosmic spaces, etc.
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54E35 Metric spaces, metrizability
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References:

[1] A. Arhangel\(^{\prime}\)skiĭ, On a class of spaces containing all metric and all locally bicompact spaces, Dokl. Akad. Nauk SSSR 151 (1963), 751 – 754 (Russian).
[2] A. V. Arhangel\(^{\prime}\)skiĭ, Mappings and spaces, Russian Math. Surveys 21 (1966), no. 4, 115 – 162. · Zbl 0171.43603 · doi:10.1070/RM1966v021n04ABEH004169
[3] R. H. Bing, Metrization of topological spaces, Canadian J. Math. 3 (1951), 175 – 186. · Zbl 0042.41301
[4] Garrett Birkhoff, Lattice Theory, American Mathematical Society Colloquium Publications, vol. 25, revised edition, American Mathematical Society, New York, N. Y., 1948. · Zbl 0033.10103
[5] Carlos J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1 – 16. · Zbl 0175.19802
[6] Carlos J. R. Borges, On metrizability of topological spaces, Canad. J. Math. 20 (1968), 795 – 804. · Zbl 0167.21201 · doi:10.4153/CJM-1968-078-1
[7] -, Elastic spaces are monotonically normal, Notices Amer. Math. Soc. 18 (1971), 840. Abstract #71T-G158.
[8] -, Four generalizations of stratifiable spaces, Proc. Third Prague Topology Sympos. 1971 (to appear).
[9] D. K. Burke and R. A. Stoltenberg, A note on \?-spaces and Moore spaces, Pacific J. Math. 30 (1969), 601 – 608. · Zbl 0183.27502
[10] Eduard Čech, On bicompact spaces, Ann. of Math. (2) 38 (1937), no. 4, 823 – 844. · Zbl 0017.42803 · doi:10.2307/1968839
[11] -, Topological spaces, Publ. House Czech Acad. Sci., Prague, 1966; English transl., Wiley, New York, 1966. MR 35 #2254.
[12] Geoffrey D. Creede, Concerning semi-stratifiable spaces, Pacific J. Math. 32 (1970), 47 – 54. · Zbl 0189.23304
[13] Z. Frolíik, On the topological product of paracompact spaces, Czechoslovak Math. J. 9 (84) (1959), 172-217. (Russian) MR 21 #3821. · Zbl 0098.14201
[14] R. W. Heath, Semi-metrizable spaces and related topic, Topology Conference, Arizona State University, Tempe, Ariz., 1967, pp. 153-161.
[15] R. W. Heath, An easier proof that a certain countable space is not stratifiable., Proc. Washington State Univ. Conf. on General Topology (Pullman, Wash., 1970), Pi Mu Epsilon, Dept. of Math., Washington State Univ., Pullman, Wash., 1970, pp. 56 – 59. · Zbl 0197.48503
[16] -, An \( {\aleph _0}\)-space which is not stratifiable, Notices Amer. Math. Soc. 17 (1970), 1040, Abstract #679-G24.
[17] R. W. Heath and D. J. Lutzer, A note on monotone normality, Notices Amer. Math. Soc. 18 (1971), 783. Abstract #687-54-1.
[18] -, A characterization of monotone normality, Notices Amer. Math. Soc. 18 (1971), 1066. Abstract #689-G8.
[19] Miroslaw Katětov, Complete normality of Cartesian products, Fund. Math. 35 (1948), 271 – 274. · Zbl 0031.28301
[20] David J. Lutzer, On generalized ordered spaces, Proc. Washington State Univ. Conf. on General Topology (Pullman, Wash., 1970), Pi Mu Epsilon, Dept. of Math., Washington State Univ., Pullman, Wash., 1970, pp. 102 – 110. · Zbl 0196.26103
[21] D. J. Lutzer and H. R. Bennett, Separability, the countable chain condition and the Lindelöf property in linearly orderable spaces, Proc. Amer. Math. Soc. 23 (1969), 664 – 667. · Zbl 0184.26303
[22] M. J. Mansfield, Some generalizations of full normality, Trans. Amer. Math. Soc. 86 (1957), 489 – 505. · Zbl 0078.14803
[23] E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375 – 376. · Zbl 0114.38904
[24] E. Michael, ℵ\(_{0}\)-spaces, J. Math. Mech. 15 (1966), 983 – 1002. · Zbl 0148.16701
[25] Kiiti Morita, Products of normal spaces with metric spaces, Math. Ann. 154 (1964), 365 – 382. · Zbl 0117.39803 · doi:10.1007/BF01362570
[26] R. H. Sorgenfrey, On the topological product of paracompact spaces, Bull. Amer. Math. Soc. 53 (1947), 631 – 632. · Zbl 0031.28302
[27] Lynn A. Steen, A direct proof that a linearly ordered space is hereditarily collectionwise normal, Proc. Amer. Math. Soc. 24 (1970), 727 – 728. · Zbl 0189.53103
[28] L. B. Treybig, Concerning continuous images of compact ordered spaces, Proc. Amer. Math. Soc. 15 (1964), 866 – 871. · Zbl 0124.15702
[29] P. Zenor, Monotonically normal spaces, Notices Amer. Math. Soc. 17 (1970), 1034, Abstract #679-G2.
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