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 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.

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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