Further study on $L$-fuzzy Q-convergence structures

Document Type: Research Paper

Author

School of Mathematics, Beijing Institute of Technology, 5 South Zhong- guancun Street, Haidian District, 100081 Beijing, P.R. China

Abstract

In this paper, we discuss the equivalent conditions of
 pretopological and topological $L$-fuzzy Q-convergence structures
 and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence
 space. {Furthermore, $L$-ordered Q-convergence
 structure is introduced and its relation with $L$-fuzzy Q-convergence
 structure is studied in a categorical sense}.

Keywords


bibitem{adame}J. Ad'{a}mek, H. Herrlich and G. E. Strecker, {it Abstract and
concrete categories}, Wiley, New York, 1990.

bibitem{burt}M. H. Burton, M. Muraleetharan and J. Gutierrez Garcia, {it Generalized
filters I}, Fuzzy Sets and Systems, {bf 106} (1999), 275--284.


bibitem{eklu1}P. Eklund and W. G"{a}hler, {it Basic notions for fuzzy topology
I}, Fuzzy Sets and Systems, {bf 26} (1988), 333--356.

bibitem{eklu2}P. Eklund and W. G"{a}hler, {it Basic notions for fuzzy topology
II}, Fuzzy Sets and Systems, {bf 27} (1988), 171--195.

{bibitem{eklu3}P. Eklund and W. G"{a}hler, {it Fuzzy filter functor and
convergence}, In: S.E. Rodabaugh, E. P. Klement, U. H"{o}hle, eds.,
Applications of Category Theory to Fuzzy Subsets, Kluwer Academic
Publishers, Dordrecht, 1992.}

bibitem{fang}J. M. Fang, {it Stratified $L$-ordered convergence
structures}, Fuzzy Sets and Systems, {bf 161(16)} (2010), 2130--2149.

bibitem{fang1}J. M. Fang, {it Relationships between $L$-ordered convergence
structures and strong $L$-topologies}, Fuzzy Sets and Systems, {bf
161}textbf{(22)} (2010), 2923--2944.

bibitem{fis}H. R. Fischer, {it Limer"{a}ume}, Math. Ann., {bf 137} (1959), 269--303.

%bibitem{wga1}W. G"{a}hler, {it Grundstrukturen der Analysis
%I,II,} Birkhh"{a}user, Basel and Stuttgart, 1977.

bibitem{wga2}W. G"{a}hler, {it The general fuzzy filter approach to fuzzy
topology I}, Fuzzy Sets and Systems, {bf 76} (1995), 205--224.

bibitem{wga3}W. G"{a}hler, {it The general fuzzy filter approach to fuzzy
topology II}, Fuzzy Sets and Systems, {bf 76} (1995), 225--246.

bibitem{gulog}M. G"{u}lou{g}lu and D. Coker, {it Convergence in $I$-fuzzy topological spaces}, Fuzzy Sets and Systems, {bf 151} (2005), 615--623.

bibitem{hohle}U. H"{o}hle and A. P. u{S}ostak, {it Axiomatic foudations of fixed-basis fuzzy topology},
In: U. H"{o}hle, S. E. Rodabaugh, eds., Mathematics of Fuzzy Sets:
Logic, Topology, and Measure Theory, Handbook Series, Kluwer
Academic Publishers, Boston, Dordrecht, London, {bf 3} (1999), 123--173.

{bibitem{jager1}G. J"{a}ger, {it A category of $L$-fuzzy convergence
spaces}, Quaest. Math., {bf 24} (2001), 501--517.}

bibitem{jager2}G. J"{a}ger, {it Subcategories of lattice--valued convergence
spaces}, Fuzzy Sets and Systems, {bf 156} (2005), 1--24.

bibitem{jager3}G. J"{a}ger, {it Pretopological and topological lattice-valued convergence
spaces}, Fuzzy Sets and Systems, {bf 158} (2007), 424--435.

bibitem{jager4}G. J"{a}ger, {it Lattice--valued convergence
spaces and regularity}, Fuzzy Sets and Systems, {bf 159} (2008), 2488--2502.

%bibitem{kent}D.C. Kent, {it Convergence functions and their related
%topologies}, Fund. Math., {bf 54}(1964), 125--133.
%
%bibitem{kowa}H.J. Kowalsky, {it Limesr"{a}ume and
%Komplettierung}, Math. Nachr., {bf 12}(1954), 301--340.

bibitem{lee1}B. Y. Lee, J. H. Park and B. H. Park, {it Fuzzy convergence structures}, Fuzzy Sets and Systems, {bf 56} (1993), 309--315.

bibitem{lee2}B. Y. Lee, S. H. Sohn and J. H. Park, {it Separation axioms of
fuzzy convergence spaces}, Fuzzy Sets and Systems, {bf 75} (1995), 111--115.

bibitem{lee3}B. Y. Lee and S. H. Sohn, {it Fuzzy regular convergence structures}, Fuzzy Sets and Systems, {bf 101} (1999), 505--508.

bibitem{lil3}L. Q. Li and Q. Jin, {it On stratified $L$-convergence spaces: Pretopological axioms
and diagonal axioms}, Fuzzy Sets and Systems, {bf 204} (2012), 40--52.

bibitem{lowen1}E. Lowen, R. Lowen and P. Wuyts, {it The categorical topological
approach to fuzzy topology and fuzzy convergence}, Fuzzy Sets and Systems, {bf 40} (1991), 347--373.

bibitem{lowen2}E. Lowen and R. Lowen, {it A topological universe extension of
FTS}, in cite{eklu3}.

bibitem{mink}J. Minkler, G. Minkler and G. Richardson, {it Regularity in
fuzzy congvergence spaces}, Fuzzy Sets and Systems, {bf 127} (2002), 281--289.

bibitem{pang}B. Pang and J. M. Fang, {it $L$-fuzzy Q-convergence
structures}, Fuzzy Sets and Systems, {bf 182} (2011), 53--65.

%bibitem{popp}H. Poppe, {it Compactness in general function spaces},
%VEB Deutscher Verlag der Wissenschaften, Berlin, 1974.
%
%bibitem{pres}G. Preuss, {it Semiuniform convergence
%spaces}, Math. Japonica, {bf 41}(1995), 465--491.

bibitem{rama}A. A. Ramadam, {it Smooth filter structures}, J. Fuzzy
Math., {bf 5} (1997), 297--308.

bibitem{wu} W. C. Wu and J. M. Fang, {it $L$-ordered fuzzifying convergence spaces}, Iranian Journal of Fuzzy Systems, {bf 9(2)} (2012), 147--161.

bibitem{xu}L. S. Xu, {it Characterizations of fuzzifying topologies by some limit structures}, Fuzzy Sets and Systems, {bf 123} (2001), 169--176.

bibitem{yao1}W. Yao, {it On many-valued stratified $L$-fuzzy convergence spaces}, Fuzzy Sets and Systems, {bf 159} (2008), 2503--2519.

bibitem{yao}W. Yao, {it On $L$-fuzzifying convergence spaces}, Iranian Journal of Fuzzy Systems, {bf 6(1)}(2009), 63--80.