Abstract
In this paper, the concept of extensional L-fuzzy Q-convergence structures is proposed. It is shown that there is an adjunction between the category of extensional L-fuzzy topological spaces and the category of extensional L-fuzzy topological spaces. In particular, the category of extensional L-fuzzy topological spaces can be embedded in the category of extensional L-fuzzy Q-convergence spaces as a reflective subcategory. Also, the notion of topological extensional L-fuzzy Q-convergence spaces is introduced and the resulting category is shown to be isomorphic to the category of extensional L-fuzzy topological spaces.
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References
1.
Fang
J.M.
, Categories isomorphic to L-FTOP , Fuzzy Sets Syst 157 (2006 ), 820 –831 .
2.
Fang
J.M.
, Stratified L -ordered convergence structures , Fuzzy Sets Syst 161 (2010 ), 2130 –2149 .
3.
Fang
J.M.
, Relationships between L -ordered convergence structures and strong L-topologies , Fuzzy Sets Syst 161 (2010 ), 2923 –2944 .
4.
Güloğlu
M.
, and
Coker
D.
, Convergence in I -fuzzy topological spaces , Fuzzy Sets Syst 151 (2005 ), 615 –623 .
5.
Höhle
U.
, and
Šostak
A.P.
, Axiomatic foudations of fixed-basis fuzzy topology , in:
Höhle
U.
,
Rodabaugh
S.E.
, (Eds.), Mathematics of Fuzzy Sets: Logic Toology, and Measure Theory, Handbook Series , vol. 3 , Kluwer Academic Publishers , Boston, Dordrecht, London , 1999 , pp. 123 –173 .
6.
Jäger
G.
, A category of L -fuzzy convergence spaces , Quaest Math 24 (2001 ), 501 –517 .
7.
Jäger
G.
, Subcategories of lattice-valued convergence spaces , Fuzzy Sets Syst 156 (2005 ), 1 –24 .
8.
Jäger
G.
, Pretopological and topological lattice-valued convergence spaces , Fuzzy Sets Syst 158 (2007 ), 424 –435 .
9.
Jäger
G.
, Lattice-valued convergence spaces and regularity , Fuzzy Sets Syst 159 (2008 ), 2488 –2502 .
10.
Jäger
G.
, Fischer’s diagonal condition for lattice-valued convergence spaces , Quaest Math 31 (2008 ), 11 –25 .
11.
Jäger
G.
, Compactification of lattice-valued convergence spaces , Fuzzy Sets Syst 161 (2010 ), 1002 –1010 .
12.
Jäger
G.
, Compactness in lattice-valued function spaces , Fuzzy Sets Syst 161 (2010 ), 2962 –2974 .
13.
Jäger
G.
, A one-point compactification for lattice-valued convergence spaces , Fuzzy Sets Syst 190 (2012 ), 21 –31 .
14.
Jäger
G.
, Largest and smallest T2-compactifications of latticevalued convergence spaces , Fuzzy Sets Syst 190 (2012 ), 32 –46 .
15.
Kubiak
T.
, On fuzzy topologies , Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, 1985 .
16.
Lowen
E.
,
Lowen
R.
, and
Wuyts
P.
, The categorical topological approach to fuzzy topology and fuzzy convergence , Fuzzy Sets Syst 40 (1991 ), 347 –373 .
17.
Li
L.Q.
, and
Jin
Q.
, On adjunctions between Lim , S L -Top , and S L -Lim , Fuzzy Sets Syst 182 (2011 ), 66 –78 .
18.
Li
L.Q.
, and
Jin
Q.
, On stratified-convergence spaces: Pretopological axioms and diagonal axioms , Fuzzy Sets Syst 204 (2012 ), 40 –52 .
19.
Li
L.Q.
, and
Jin
Q.
, p -Topologicalness and p -regularity for latticevalued convergence spacesFuzzy Sets Syst 238 (2014 ), 26 –45 .
20.
Li
L.Q.
,
Jin
Q.
, and
Hu
K.
, On stratified L -convergence spaces: Fischer’s diagonal axiom , Fuzzy Sets Syst 267 (2015 ), 31 –40 .
21.
Min
K.C.
, Fuzzy limit spaces , Fuzzy Sets Syst 32 (1989 ), 343 –357 .
22.
Pang
B.
, and
Fang
J.M.
, L -fuzzy Q-convergence structuresFuzzy Sets Syst 182 (2011 ), 53 –65 .
23.
Pang
B.
, Further study on L -fuzzy Q-convergence structures , Iran J Fuzzy Syst 10 (5 ) (2013 ), 149 –166 .
24.
Pang
B.
, On (L, M )-fuzzy convergence spaces , Fuzzy Sets Syst 238 (2014 ), 46 –70 .
25.
Pang
B.
, and
Shi
F.-G.
, Degrees of compactness of (L, M )-fuzzy convergence spaces and its applications , Fuzzy Sets Syst 251 (2014 ), 1 –22 .
26.
Pang
B.
, Enriched (L, M )-fuzzy convergence spaces , J Intell Fuzzy Syst 27 (2014 ), 93 –103 .
27.
Preuss
G.
, Foundations of Topology-An Approach to Convenient Topology , Kluwer Academic Publisher , Dordrecht, Boston, London , 2002 .
28.
Šostak
A.P.
, On a fuzzy topological structure , Suppl Rend Circ Mat Palermo Ser II 11 (1985 ), 89 –103 .
29.
Wu
W.C.
, and
Fang
J.M.
, L -ordered fuzzifying convergence spacesIran J Fuzzy Syst 9 (2 ) (2012 ), 147 –161 .
30.
Xu
L.S.
, Characterizations of fuzzifying topologies by some limit structures , Fuzzy Sets Syst 123 (2001 ), 169 –176 .
31.
Yao
W.
, On many-valued stratified L -fuzzy convergence spaces , Fuzzy Sets Syst 159 (2008 ), 2503 –2519 .
32.
Yao
W.
, On L -fuzzifying convergence spaces , Iran J Fuzzy Syst 6 (1 ) (2009 ), 63 –80 .