A Contribution to the Theory of Metrization
Canadian journal of mathematics, Tome 29 (1977) no. 6, pp. 1145-1151

Voir la notice de l'article provenant de la source Cambridge University Press

In a paper on the same subject [28] and another coming out at the same time [27], Nagata gave his celebrated Double (treble, really) Sequence Theorem, with which he deduced easily and thus brought together the basic metrization theorems, i.e. theorems in which the conditions for metrizability are given as the availability of bases or subbases of certain descriptions.
Hung, H. H. A Contribution to the Theory of Metrization. Canadian journal of mathematics, Tome 29 (1977) no. 6, pp. 1145-1151. doi: 10.4153/CJM-1977-113-6
@article{10_4153_CJM_1977_113_6,
     author = {Hung, H. H.},
     title = {A {Contribution} to the {Theory} of {Metrization}},
     journal = {Canadian journal of mathematics},
     pages = {1145--1151},
     year = {1977},
     volume = {29},
     number = {6},
     doi = {10.4153/CJM-1977-113-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-113-6/}
}
TY  - JOUR
AU  - Hung, H. H.
TI  - A Contribution to the Theory of Metrization
JO  - Canadian journal of mathematics
PY  - 1977
SP  - 1145
EP  - 1151
VL  - 29
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-113-6/
DO  - 10.4153/CJM-1977-113-6
ID  - 10_4153_CJM_1977_113_6
ER  - 
%0 Journal Article
%A Hung, H. H.
%T A Contribution to the Theory of Metrization
%J Canadian journal of mathematics
%D 1977
%P 1145-1151
%V 29
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-113-6/
%R 10.4153/CJM-1977-113-6
%F 10_4153_CJM_1977_113_6

[1] 1. Alexandroff, P. S. and Urysohn, P., Une condition nécessaire et suffisante pour qu'une class soit une class (@), C. R. Acad. Sci., Paris, 177 (1923), 1274–1277. Google Scholar

[2] 2. Arhangel'skii, A. V., New criteria for paracompactness and metrizability of an arbitrary T\ space, Dokl. Akad. Nauk SSSR lp (1961), 13-15; Soviet Math. Dokl. 2 (1961), 1367–1369. Google Scholar

[3] 3. Arhangel'skii, A. V. Bicompact sets and the topology of spaces, Dokl. Akad. Nauk SSSR 150 (1963), 9-12 ; Soviet Math. Dokl. 4 (1963), 561–564. Google Scholar

[4] 4. Arhangel'skii, A. V. Bicompact sets and the topology of spaces, Trudy, Moskov. Mat. Obsc. 13 (1965), 3-55; Trans. Moscow Math. Soc. 13 (1965), 1–62. Google Scholar

[5] 5. Arhangel'skii, A. V. Mappings and spaces, Uspehi Mat. Nauk 21 (1966), 133–184; Russian Math. Surveys 01 (1966), no.4,115-162. Google Scholar

[6] 6. Bing, R. H., Metrization of topological spaces, Can. J. Math. 3 (1951), 175–186. Google Scholar

[7] 7. Céder, J. G., Some generalizations of metric spaces, Pac. J. Math. 11 (1961), 105–126. Google Scholar

[8] 8. Comfort, W. W. and Negrepontis, S., The theory of ultrafilters, Die Grundlehren der math. Wissenschaften Band 211 (Springer-Verlag, Berlin and New York, 1974). Google Scholar

[9] 9. Frink, A. H., Distance junctions and the metrization problem, Bull. Amer. Math. Soc. 10 (1937), 133–142. Google Scholar

[10] 10. Harley, P. W. III and Faulkner, G. D., Metrization of symmetric spaces, Can. J. Math. 27 (1975) 986–990. Google Scholar

[11] 11. Heath, R. W., On open mappings and certain spaces satisfying the first countability axiom, Fundamenta Mathematicae 57 (1965), 91–96. Google Scholar

[12] 12. Hodel, R. E., Metrizability of topological spaces, Pac. J. Math. 55 (1974), no. 2, 441–459. Google Scholar

[13] 13. Hung, H. H., Some metrization theorems, Proc. Amer. Math. Soc. 54 (1976), 363–367. Google Scholar

[14] 14. Hung, H. H. Improvements on some earlier metrization theorems, (unpublished) 1975. Google Scholar

[15] 15. Hung, H. H. One more metrization theorem, Proc. Amer. Math. Soc. 57 (1976), 351–353. Google Scholar

[16] 16. Jones, F. B., R. L. Moore's axiom 1’ and metrization, Proc. Amer. Math. Soc. 9 (1958), 487. Google Scholar

[17] 17. Jones, F. B. Metrization, Amer. Math. Monthly 73 (1966), 571–576. Google Scholar

[18] 18. Martin, H. W., Metrization of symmetric spaces and regular maps, Proc. Amer. Math. Soc. 35 (1972), 269–274. Google Scholar

[19] 19. Martin, H. W. A note on the Frink metrization theorem, Rocky Mountain Jour. Math. 6 (1976), 155–157. Google Scholar

[20] 20. Martin, H. W. Weak bases and metrization, Trans. Amer. Math. Soc. 222 (1976), 337–344. Google Scholar

[21] 21. Michael, E., A note on paracompact spaces, Proc. Amer. Math. Soc. 4 (1953), 831–838. Google Scholar

[22] 22. Michael, E. Another note on paracompact spaces, Proc. Amer. Math. Soc. 8 (1957), 822–828. Google Scholar

[23] 23. Michael, E. Yet another note on paracompact spaces, Proc. Amer. Math. Soc. 10 (1959), 309–314. Google Scholar

[24] 24. Michael, E. \ta-spaces, J. Math. Mech. 15 (1966), 985–1002. Google Scholar

[25] 25. Morita, K., A condition for the metrizability of topological spaces and for n-dimensionality, Sci. Rep. Tokyo Kyoiki Daigaku, Ser. A, 5 (1955), 33–36. Google Scholar

[26] 26. Nagata, J., On a necessary and sufficient condition for metrizability, J. Inst. Polytech. Osaka City Univ. Ser. A Math. 1 (1950), 93–100. Google Scholar

[27] 27. Nagata, J. A theorem for metrizability of a topological space, Proc. Japan Acad. 33 (1957), 128- 130. Google Scholar

[28] 28. Nagata, J. A contribution to the theory of metrization, J. Inst. Polytech., Osaka City Univ. 8 (1957), 185–192. Google Scholar

[29] 29. Nagata, J. Modern general topology (North-Holland, Amsterdam, second edition, 1974). Google Scholar

[30] 30. Nagami, K., Note on metrizability and n-dimensionality, Proc. Japan Acad. 36 (1960), 565–570. Google Scholar

[31] 31. Nagami, K. a-spaces and product spaces, Math. Ann. 181 (1969), 109–118. Google Scholar

[32] 32. Niemytzki, V., On the third axiom of metric spaces, Trans. Amer. Math. Soc. 29 (1927), 507–513. Google Scholar

[33] 33. O'Meara, P. A., A metrization theorem, Math. Nach. 45 (1970), 69–72. Google Scholar

[34] 34. Smirnov, Ju. M., A necessary and sufficient condition for metrizability of a topological space, Dokl. Akad. SSSR (N.S.) 77 (1951), 197–200. (Russian). Google Scholar

[35] 35. Stone, A. H., Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948). 977–982. Google Scholar

[36] 36. Stone, A. H. Sequences of coverings, Pacific J. Math. 10 (1960), 689–691. Google Scholar

[37] 37. Wilson, W. A., On semi-metric spaces, Amer. J. Math. 53 (1931), 361–373. Google Scholar

Cité par Sources :