Geodesic
Characterization of Certain Classes of Spaces With Gδ Points as Open Images of Metric Spaces
Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1229-1238

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

The study of metrization has led to the development of a number of new topological spaces, called generalized metric spaces, within the past fifteen years. For a survey of results in metrization theory involving many of these spaces, the reader is referred to [13]. Quite a few of these generalized metric spaces have been studied extensively, somewhat independently of their role in metrization theorems. Specifically, we refer here to characterizations of these spaces by various workers as images of metric spaces. Results in this area have been obtained by Alexander [2], Arhangel'skii [3], Burke [5], Heath [10], Michael [15], Nagata [16], and the author [1], to mention a few. Later we will recall specifically some of these results. 
Abernethy, Kenneth C. Characterization of Certain Classes of Spaces With Gδ Points as Open Images of Metric Spaces. Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1229-1238. doi: 10.4153/CJM-1975-128-3
@article{10_4153_CJM_1975_128_3,
     author = {Abernethy, Kenneth C.},
     title = {Characterization of {Certain} {Classes} of {Spaces} {With} {G\ensuremath{\delta}} {Points} as {Open} {Images} of {Metric} {Spaces}},
     journal = {Canadian journal of mathematics},
     pages = {1229--1238},
     year = {1975},
     volume = {27},
     number = {6},
     doi = {10.4153/CJM-1975-128-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-128-3/}
}
TY  - JOUR
AU  - Abernethy, Kenneth C.
TI  - Characterization of Certain Classes of Spaces With Gδ Points as Open Images of Metric Spaces
JO  - Canadian journal of mathematics
PY  - 1975
SP  - 1229
EP  - 1238
VL  - 27
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-128-3/
DO  - 10.4153/CJM-1975-128-3
ID  - 10_4153_CJM_1975_128_3
ER  - 
%0 Journal Article
%A Abernethy, Kenneth C.
%T Characterization of Certain Classes of Spaces With Gδ Points as Open Images of Metric Spaces
%J Canadian journal of mathematics
%D 1975
%P 1229-1238
%V 27
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-128-3/
%R 10.4153/CJM-1975-128-3
%F 10_4153_CJM_1975_128_3

[1] 1. Abernethy, Kenneth, On characterizing certain classes of first countable spaces by open mappings, Pacific J. Math. 53 (1974), 319–326. Google Scholar

[2] 2. Alexander, Charles C., Semi-developable spaces and quotient images of metric spaces, Pacific J. Math. 87 (1971), 277–293. Google Scholar

[3] 3. Arhangel, A. V.'skii, Mappings and spaces, Russian Math. Surveys 21 (1966), 115–162. Google Scholar

[4] 4. Borges, Carlos J., On stratifiable spaces, Pacific J. Math. 17 (1966), 1–16. Google Scholar

[5] 5. Burke, Dennis K., Cauchy sequences in semi-metric spaces, Proc. Amer. Math. Soc. 33 (1972), 161–165. Google Scholar

[6] 6. Ceder, Jack, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105–125. Google Scholar

[7] 7. Creede, Geoffrey C., Concerning semi-stratifiable spaces, Pacific J. Math. 32 (1970), 47–54. Google Scholar

[8] 8. Hanai, S., On open mappings, II, Proc. Japan Acad. 37 (1961), 233–238. Google Scholar

[9] 9. Heath, R. V., Arc-wise connectedness in semi-metric spaces, Pacific J. Math. 12 (1962), 1301–1319. Google Scholar

[10] 10. Heath, R. V., On open mappings and certain spaces satisfying the first countability axiom, Fund. Math. 57 (1965), 91–96. Google Scholar

[11] 11. Heath, R. V., An easier proof that a certain countable space is not stratifiable, Proc. Wash. State Univ. Conference on General Topology (1970), 56–59. Google Scholar

[12] 12. Hodel, R. E., Spaces defined by sequences of open covers which guarantee that certain sequences have cluster points, Duke Math. J. 39 (1972), 253–265. Google Scholar

[13] 13. Hodel, R. E., Some results in metrization theory, 1950–1972, Proceedings of the U.P.I. Topology Conference, 1973 (Springer-Verlag Lecture Notes in Mathematics, 875 (1974)). Google Scholar

[14] 14. Lutzer, David, Semi-metrizable and stratifiable spaces, General Topology and Appl. 1 (1971), 43–48. Google Scholar

[15] 15. Michael, E. A., On representing spaces as images of metrizable and related spaces, General Topology and Appl. 1 (1971), 329–344. Google Scholar

[16] 16. Nagata, Jun-iti, On generalized metric spaces and q-closed mappings, to appear. Google Scholar

[17] 17. Ponomarev, V. I., Axioms of countability and continuous mappings, Bull. Pol. Akad. Nauk. 8 (1960), 127–134. Google Scholar

Cité par Sources :