Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
proximity; metrizable proximity
proximity; metrizable proximity
Summary:
It is shown that any proximity that is generated by a countable family of entourages is sequential. Metrization theorems for proximities are derived.
References:
[1] Choban M., Nedev S.: On some classes of proximity spaces and their metrization (in Russian). C. R. Acad. Bulgare Sci. 27 , 5 (1974), 591-598. MR 0353266
[2] Efremovich V.A.: The geometry of proximity (in Russian). Mat. Sb. 31 , 1 (1952), 189-200. MR 0055659
[3] Efremovich V.A., Schvarz A.S.: A new definition of uniform spaces, a metrization of proximity spaces (in Russian). Dokl. Akad. Nauk SSSR 89 , 3 (1953), 393-396. MR 0061369
[4] Hadjiivanov N., Nedev S.: O-metrizable proximities are metrizable (in Russian). C.R. Acad. Bulgare Sci. 26 , 10 (1973), 1285-1291.
[5] Hušek M.: Factorization of mappings (products of proximally fine spaces). Seminar Uniform Spaces 1973-74 directed by Z. Frolík, Math. Inst. ČSAV Prague, 1974, pp.173-190. MR 0391022 | Zbl 0327.54023
[6] Ivanov S.: Uniformization of proximity topologies (in Russian). C.R. Acad. Bulgare Sci. 28 , 2 (1975), 147-149. MR 0370513
[7] Nedev S., Vilímovský J.: A note on regularity and metrizability of proximities. C.R. Acad. Bulgare Sci. 41 , 5 (1988), 13-14. MR 0952202
[8] Ramm I., Švarc A.S.: Geometry of proximity, uniform geometry and topology (in Russian). Mat. Sb. 33 (1953), 157-180. MR 0061368
[9] Smirnov J.M.: On proximity spaces (in Russian). Dokl. Akad. Nauk SSSR 84 (1952), 895-898. MR 0055660
[10] Vilhelm V., Vitner Č.: Continuity in metric spaces (in Czech). Čas. pěst. mat. 77 (1952), 147-173. MR 0060215
Search
Partner of
