On proximities generated by countable families of entourages

Svetlozar Ivanov; Jan Pelant; S. Nedev

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 3, page 535-541
  • ISSN: 0010-2628

Abstract

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It is shown that any proximity that is generated by a countable family of entourages is sequential. Metrization theorems for proximities are derived.

How to cite

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Ivanov, Svetlozar, Pelant, Jan, and Nedev, S.. "On proximities generated by countable families of entourages." Commentationes Mathematicae Universitatis Carolinae 45.3 (2004): 535-541. <http://eudml.org/doc/249373>.

@article{Ivanov2004,
abstract = {It is shown that any proximity that is generated by a countable family of entourages is sequential. Metrization theorems for proximities are derived.},
author = {Ivanov, Svetlozar, Pelant, Jan, Nedev, S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {proximity; metrizable proximity; proximity; metrizable proximity},
language = {eng},
number = {3},
pages = {535-541},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On proximities generated by countable families of entourages},
url = {http://eudml.org/doc/249373},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Ivanov, Svetlozar
AU - Pelant, Jan
AU - Nedev, S.
TI - On proximities generated by countable families of entourages
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 3
SP - 535
EP - 541
AB - It is shown that any proximity that is generated by a countable family of entourages is sequential. Metrization theorems for proximities are derived.
LA - eng
KW - proximity; metrizable proximity; proximity; metrizable proximity
UR - http://eudml.org/doc/249373
ER -

References

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  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. (1974) MR0353266
  2. Efremovich V.A., The geometry of proximity (in Russian), Mat. Sb. 31 , 1 (1952), 189-200. (1952) MR0055659
  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. (1953) MR0061369
  4. Hadjiivanov N., Nedev S., O-metrizable proximities are metrizable (in Russian), C.R. Acad. Bulgare Sci. 26 , 10 (1973), 1285-1291. (1973) 
  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. Zbl0327.54023MR0391022
  6. Ivanov S., Uniformization of proximity topologies (in Russian), C.R. Acad. Bulgare Sci. 28 , 2 (1975), 147-149. (1975) MR0370513
  7. Nedev S., Vilímovský J., A note on regularity and metrizability of proximities, C.R. Acad. Bulgare Sci. 41 , 5 (1988), 13-14. (1988) MR0952202
  8. Ramm I., Švarc A.S., Geometry of proximity, uniform geometry and topology (in Russian), Mat. Sb. 33 (1953), 157-180. (1953) MR0061368
  9. Smirnov J.M., On proximity spaces (in Russian), Dokl. Akad. Nauk SSSR 84 (1952), 895-898. (1952) MR0055660
  10. Vilhelm V., Vitner Č., Continuity in metric spaces (in Czech), Čas. pěst. mat. 77 (1952), 147-173. (1952) MR0060215

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