| Title:
|
On proximities generated by countable families of entourages (English) |
| Author:
|
Ivanov, S. |
| Author:
|
Pelant, J. |
| Author:
|
Nedev, S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
535-541 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that any proximity that is generated by a countable family of entourages is sequential. Metrization theorems for proximities are derived. (English) |
| Keyword:
|
proximity |
| Keyword:
|
metrizable proximity |
| MSC:
|
54E05 |
| idZBL:
|
Zbl 1100.54020 |
| idMR:
|
MR2103147 |
| . |
| Date available:
|
2009-05-05T16:47:12Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119480 |
| . |
| Reference:
|
[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 |
| Reference:
|
[2] Efremovich V.A.: The geometry of proximity (in Russian).Mat. Sb. 31 , 1 (1952), 189-200. MR 0055659 |
| Reference:
|
[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 |
| Reference:
|
[4] Hadjiivanov N., Nedev S.: O-metrizable proximities are metrizable (in Russian).C.R. Acad. Bulgare Sci. 26 , 10 (1973), 1285-1291. |
| Reference:
|
[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. Zbl 0327.54023, MR 0391022 |
| Reference:
|
[6] Ivanov S.: Uniformization of proximity topologies (in Russian).C.R. Acad. Bulgare Sci. 28 , 2 (1975), 147-149. MR 0370513 |
| Reference:
|
[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 |
| Reference:
|
[8] Ramm I., Švarc A.S.: Geometry of proximity, uniform geometry and topology (in Russian).Mat. Sb. 33 (1953), 157-180. MR 0061368 |
| Reference:
|
[9] Smirnov J.M.: On proximity spaces (in Russian).Dokl. Akad. Nauk SSSR 84 (1952), 895-898. MR 0055660 |
| Reference:
|
[10] Vilhelm V., Vitner Č.: Continuity in metric spaces (in Czech).Čas. pěst. mat. 77 (1952), 147-173. MR 0060215 |
| . |
