On a theorem of Arhangelskiĭ
Author:
H. H. Hung
Journal:
Proc. Amer. Math. Soc. 82 (1981), 629633
MSC:
Primary 54D18; Secondary 54E35
MathSciNet review:
614891
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Abstract: We define a class of spaces which is more extensive than the class of BCO spaces and which counts among its members some that are not even first countable, and show that this more extensive class of spaces nevertheless intersects the class of paracompact Hausdorff spaces at precisely the class of metrizable spaces as does the class of BCO spaces, thus extending a theorem of Arhangel'skiĭ. We further show that this extension of Arhangel'skiĭ's result has gone the farthest in the sense that any class of spaces that meets the paracompact spaces at precisely the metrizable spaces must, among the Hausdorff spaces, be smaller than the class we have defined.
 [1]
A.
V. Arhangel′skiĭ, Some metrization theorems,
Uspehi Mat. Nauk 18 (1963), no. 5 (113),
139–145 (Russian). MR 0156318
(27 #6242)
 [2]
R.
H. Bing, Metrization of topological spaces, Canadian J. Math.
3 (1951), 175–186. MR 0043449
(13,264f)
 [3]
Dennis
K. Burke and David
J. Lutzer, Recent advances in the theory of generalized metric
spaces, Topology (Proc. Ninth Annual Spring Topology Conf., Memphis
State Univ., Memphis, Tenn., 1975) Dekker, New York, 1976,
pp. 1–70. Lecture Notes in Pure and Appl. Math., Vol. 24. MR 0428293
(55 #1318)
 [4]
R.
E. Hodel, Some results in metrization theory, 1950–1972,
Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg,
Va., 1973) Springer, Berlin, 1974, pp. 120–136. Lecture Notes
in Math., Vol. 375. MR 0355986
(50 #8459)
 [5]
H.
H. Hung, A contribution to the theory of metrization, Canad.
J. Math. 29 (1977), no. 6, 1145–1151. MR 0454929
(56 #13172)
 [6]
D. König, Sur les correspondances multivoques des ensembles, Fund. Math. 8 (1926), 114134.
 [7]
E.
Michael, Yet another note on paracompact
spaces, Proc. Amer. Math. Soc. 10 (1959), 309–314. MR 0105668
(21 #4406), http://dx.doi.org/10.1090/S00029939195901056681
 [8]
R.
L. Moore, Foundations of point set theory, Revised edition.
American Mathematical Society Colloquium Publications, Vol. XIII, American
Mathematical Society, Providence, R.I., 1962. MR 0150722
(27 #709)
 [9]
J.
M. Worrell Jr. and H.
H. Wicke, Characterizations of developable topological spaces,
Canad. J. Math. 17 (1965), 820–830. MR 0182945
(32 #427)
 [1]
 A. V. Arhangel'skiĭ, Some metrization theorems, Uspehi Mat. Nauk 18 (1963), no. 5(113), 139145. (Russian) MR 0156318 (27:6242)
 [2]
 R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), 175186. MR 0043449 (13:264f)
 [3]
 D. K. Burke and D. J. Lutzer, Recent advances in the theory of generalized metric spaces, Topology (Proc. Memphis State Univ. Conf.), Dekker, New York, 1975. MR 0428293 (55:1318)
 [4]
 R. Hodel, Some results in metrization theory, 19501972 (Topology Conference, Virginia Polytechnic Inst. and State Univ., 1973), Lecture Notes in Math., Vol. 375, SpringerVerlag, Berlin and New York, 1974, pp. 120136. MR 0355986 (50:8459)
 [5]
 H. H. Hung, A contribution to the theory of metrization, Canad. J. Math. 29 (1977), 11451151. MR 0454929 (56:13172)
 [6]
 D. König, Sur les correspondances multivoques des ensembles, Fund. Math. 8 (1926), 114134.
 [7]
 E. Michael, Yet another note on paracompact spaces, Proc. Amer. Math. Soc. 10 (1959), 309314. MR 0105668 (21:4406)
 [8]
 R. L. Moore, Foundations of point set theory, Amer. Math. Soc. Colloq. Publ., vol. 13, Amer. Math. Soc., Providence, R.I., 1962. MR 0150722 (27:709)
 [9]
 J. M. Worrell, Jr. and H. H. Wicke, Characterizations of developable topological spaces, Canad. J. Math. 17 (1965), 820830. MR 0182945 (32:427)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198106148910
PII:
S 00029939(1981)06148910
Keywords:
Paracompactness,
BCO,
metrizability,
largest class to meet the paracompact at the metrizable
Article copyright:
© Copyright 1981
American Mathematical Society
