On convergence theory in fuzzy topological spaces and its applications

Nouh, Ali Ahmed

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 2, page 295-316
  • ISSN: 0011-4642

Abstract

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In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the -relation and the -neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong -compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar to the one which exists between the convergence of filters and the convergence of nets in topological spaces.

How to cite

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Nouh, Ali Ahmed. "On convergence theory in fuzzy topological spaces and its applications." Czechoslovak Mathematical Journal 55.2 (2005): 295-316. <http://eudml.org/doc/30946>.

@article{Nouh2005,
abstract = {In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the $Q$-relation and the $Q$-neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong $Q$-compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar to the one which exists between the convergence of filters and the convergence of nets in topological spaces.},
author = {Nouh, Ali Ahmed},
journal = {Czechoslovak Mathematical Journal},
keywords = {fuzzy points; $Q$-neighborhoods; fuzzy filters; fuzzy nets; limit; adherent and $Q$-adherent points of fuzzy filters and fuzzy nets; fuzzy continuity; strong $Q$-compactness; fuzzy points; -neighborhoods; fuzzy filters; fuzzy nets; limit},
language = {eng},
number = {2},
pages = {295-316},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On convergence theory in fuzzy topological spaces and its applications},
url = {http://eudml.org/doc/30946},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Nouh, Ali Ahmed
TI - On convergence theory in fuzzy topological spaces and its applications
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 2
SP - 295
EP - 316
AB - In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the $Q$-relation and the $Q$-neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong $Q$-compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar to the one which exists between the convergence of filters and the convergence of nets in topological spaces.
LA - eng
KW - fuzzy points; $Q$-neighborhoods; fuzzy filters; fuzzy nets; limit; adherent and $Q$-adherent points of fuzzy filters and fuzzy nets; fuzzy continuity; strong $Q$-compactness; fuzzy points; -neighborhoods; fuzzy filters; fuzzy nets; limit
UR - http://eudml.org/doc/30946
ER -

References

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  1. 10.2307/2307247, Amer. Math. Monthly 62 (1955), 551–557. (1955) Zbl0065.37901MR0073153DOI10.2307/2307247
  2. Fuzzy Relational Systems: Fundations and Principles, Kluwer, New York, 2002. (2002) 
  3. 10.2307/1968508, Ann. Math. 38 (1937), 39–56. (1937) Zbl0016.08502MR1503323DOI10.2307/1968508
  4. Topologie Generale, Ch. 1, Actualites Sci. Indust., Paris 858, 1940. (1940) 
  5. Théorie des filtres, C.  R.  Acad. Sci. Paris 205 (1937), 595–598. (1937) Zbl0017.24305
  6. 10.1016/0022-247X(68)90057-7, J.  Math. Anal. Appl. 24 (1968), 182–190. (1968) Zbl0167.51001MR0236859DOI10.1016/0022-247X(68)90057-7
  7. Theory of convergence in fuzzy topological spaces, J.  Fuzzy Math. 1 (1993), 1–12. (1993) MR1230301
  8. On -compact fuzzy topological spaces, J.  Fuzzy Math. 1 (1993), 321–326. (1993) MR1230323
  9. Fuzzy filter functors and convergence, Applictions of Category Theory to Fuzzy Subsets, Kluwer Academic Publishers, Dordrecht-Boston-London, 1992, pp. 109–136. (1992) MR1154570
  10. Convergence, Fuzzy Sets and Systems 73 (1995), 97–129. (1995) 
  11. The general fuzzy filter approach to fuzzy topology. Part I, Fuzzy Sets and Systems 76 (1995), 205–224. (1995) MR1365392
  12. 10.1016/0165-0114(95)00057-R, Fuzzy Sets and Systems 76 (1995), 225–246. (1995) DOI10.1016/0165-0114(95)00057-R
  13. 10.1016/0022-247X(83)90002-1, J.  Math. Anal. Appl. 94 (1983), 1–23. (1983) Zbl0512.54006MR0701446DOI10.1016/0022-247X(83)90002-1
  14. Generalized mappings between fuzzy topological spaces, Math. Pannon. 31 (1992), 59–71. (1992) MR1240878
  15. General Topology, Van Nostrand, New York, 1955. (1955) Zbl0066.16604MR0070144
  16. Generalized compactness in fuzzy topological spaces, Math. Vesnik 43 (1991), 29–40. (1991) MR1210258
  17. 10.1006/jmaa.1993.1404, J.  Math. Anal. Appl. 180 (1993), 325–341. (1993) MR1251863DOI10.1006/jmaa.1993.1404
  18. Fuzzy Sets and Fuzzy Logic: Theory and Applications, Perentice Hall, , 1995, pp. 574. (1995) MR1329731
  19. 10.1016/0022-247X(77)90223-2, J.  Math. Anal. Appl. 58 (1977), 11–21. (1977) Zbl0347.54002MR0440483DOI10.1016/0022-247X(77)90223-2
  20. 10.1016/0016-660X(79)90004-7, Gen. Topol. Appl. 10 (1979), 147–160. (1979) Zbl0409.54008MR0527841DOI10.1016/0016-660X(79)90004-7
  21. The relation between filter and net convergence in fuzzy topological spaces, Fuzzy Math. 3 (1983), 41–52. (1983) Zbl0569.54007MR0743505
  22. 10.1016/0165-0114(90)90045-8, Fuzzy Sets and Systems 37 (1990), 225–235. (1990) MR1074667DOI10.1016/0165-0114(90)90045-8
  23. 10.1016/0165-0114(92)90193-8, Fuzzy Sets and Systems 51 (1992), 203–217. (1992) MR1188312DOI10.1016/0165-0114(92)90193-8
  24. -fuzzy topological concepts, Portugaliae Math. 49 (1992), 85–108. (1992) MR1165924
  25. 10.2307/2370388, Amer. J.  Math. 44 (1922), 102–121. (1922) MR1506463DOI10.2307/2370388
  26. 10.1016/0022-247X(88)90271-5, J. Math. Anal. Appl. 129 (1988), 560–568. (1988) MR0924310DOI10.1016/0022-247X(88)90271-5
  27. -prefilter theory, Fuzzy Sets and Systems 38 (1990), 115–124. (1990) MR1078725
  28. Fuzzy topology  I, J.  Math. Anal. Appl. 76 (1980), 571–599. (1980) MR0587361
  29. Fuzzy topology  II, J.  Math. Anal. Appl. 77 (1980), 20–37. (1980) MR0591259
  30. 10.1016/0165-0114(92)90074-E, Fuzzy Sets and Systems 51 (1992), 41–51. (1992) MR1187370DOI10.1016/0165-0114(92)90074-E
  31. 10.1016/0165-0114(93)90211-Y, Fuzzy Sets and Systems 56 (1993), 309–315. (1993) MR1227900DOI10.1016/0165-0114(93)90211-Y
  32. 10.1016/S0019-9958(65)90241-X, Information and Control 8 (1965), 338–353. (1965) Zbl0139.24606MR0219427DOI10.1016/S0019-9958(65)90241-X
  33. Compactness in fuzzy topological spaces, Kuxue Tongbao 29 (1984), 582–585. (1984) Zbl0576.54008MR0834292

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