Geodesic
Separating Closed Sets by Continuous Mappings into Developable Spaces
Canadian journal of mathematics, Tome 33 (1981) no. 6, pp. 1420-1431

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

A topological space X is called developable if it has a development, i.e., a sequence of open covers of X such that for each x ∈ X the collection is a neighbourhood base of x, where This class of spaces has turned out to be one of the most natural and useful generalizations of metrizable spaces [23]. In [4] it was shown that some well known results in metrization theory have counterparts in the theory of developable spaces (i.e., Urysohn's metrization theorem, the Nagata-Smirnov theorem, and Nagata's “double sequence theorem”). Moreover, in [3] it was pointed out that subspaces of products of developable spaces (i.e., D-completely regular spaces) can be characterized in much the same way as subspaces of products of metrizable spaces (i.e., completely regular T 1-spaces). 
Brandenburg, Harald. Separating Closed Sets by Continuous Mappings into Developable Spaces. Canadian journal of mathematics, Tome 33 (1981) no. 6, pp. 1420-1431. doi: 10.4153/CJM-1981-108-1
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[1] 1. Alster, K. and Engelking, R., Subparacompactness and product spaces, Bull. Acad. Polon. Sci. 20 (1972), 763–767. Google Scholar

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

[3] 3. Brandenburg, H., On a class of nearness spaces and the epireflective hull of developable topological spaces, in: Proceedings of the International Symposium on Topology and its Appl. (Beograd, 1977), (to appear). Google Scholar

[4] 4. Brandenburg, H., Some characterizations of developable spaces, Proc. Amer. Math. Soc. 80 (1980), 157–161. Google Scholar

[5] 5. Brandenburg, H., On spaces with a Gδ-basis, Arch. Math. 35 (1980), 544–547. Google Scholar

[6] 6. Brandenburg, H., A characterization of perfect spaces, unpublished manuscript. Google Scholar

[7] 7. Chaber, J., Conditions which imply compactness in countably compact spaces, Bull. Acad. Polon. Sci. 24 (1976), 993–998. Google Scholar

[8] 8. Chaber, J., On subparacompactness and related properties, General Topol. Appl. 10 (1979), 13–17. Google Scholar

[9] 9. Heath, R. W. and Michael, E. A., A property of the Sorgenfrey line, Compositio Math. 23 (1971), 185–188. Google Scholar

[10] 10. Heldermann, N. C., The category of D-completely regular spaces is simple, Trans. Amer. Math. Soc. 262 (1980), 437–446. Google Scholar

[11] 11. Heldermann, N. C., Developability and some new regularity axioms, Can. J. Math. 33 (1981), 641–663. Google Scholar

[12] 12. Herrlich, H., A concept of nearness, General Topol. Appl. 5 (1974), 191–212. Google Scholar

[13] 13. Inokuma, T., On a characteristic property of completely normal spaces, Proc. Japan Acad. 31 (1955), 56–59. Google Scholar

[14] 14. Isbell, J. R., A note on complete closure algebras, Math. Systems Theory 3 (1969), 310–312. Google Scholar

[15] 15. Katětov, M., Complete normality of cartesian products, Fund. Math. 35 (1948), 271–274. Google Scholar

[16] 16. Misra, A. K., A topological view of P-spaces, General Topol. Appl. 2 (1972), 349–362. Google Scholar

[17] 17. Mysior, A., Two remarks on D-regular spaces, Glasnik Mat., III. Ser. 15, 35 (1980), 153–156. Google Scholar

[18] 18. Pareek, C. M., Moore spaces, semi-metric spaces and continuous mappings connected with them, Can. J. Math. 24 (1972), 1033–1042. Google Scholar

[19] 19. Pears, A. R., Dimension theory of general spaces, (Cambridge University Press, Cambridge et al., 1975). Google Scholar

[20] 20. Smirnov, Yu. M., On normally placed sets in normal spaces, Mat. Sbornik 29 (1951), 173–176, (in Russian). Google Scholar

[21] 21. Steen, L. A. and Seebach, J. A., Jr., Counterexamples in topology, (Springer Verlag, Berlin et al., 1978). Google Scholar

[22] 22. Tukey, J. W., Convergence and uniformity in topology, Ann. of Math. Studies 2 (Princeton, 1940). Google Scholar

[23] 23. Worrell, J. M., Jr. and Wicke, H. H., Characterizations of developable topological spaces, Can. J. Math. 17 (1965), 820–830. Google Scholar

[24] 24. Worrell, J. M., Jr., Upper semicontinuous decompositions of developable spaces, Proc. Amer. Math. Soc. 16 (1965), 485–490. Google Scholar

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