\bibitem{Adamek2009}
J.~Ad{\'{a}}mek, H.~Herrlich and G.~E. Strecker, {\it Abstract and Concrete
Categories: the joy of cats}, Dover Publications, New York, 2009.
\bibitem{Aerts1999}
D.~Aerts, {\it Foundations of quantum physics: a general realistic and operational approach}, Int. J. Theor. Phys., {\bf 38}\textbf{(1)} (1999), 289-358.
\bibitem{Aerts1999a}
D.~Aerts, E.~Colebunders, A.~van~der Voorde and B.~van Steirteghem, {\it State property systems and closure spaces: a study of categorical equivalence}, Int. J. Theor. Phys., {\bf 38}\textbf{(1)} (1999), 359-385.
\bibitem{Aerts2002}
D.~Aerts, E.~Colebunders, A.~van~der Voorde and B.~van Steirteghem, {\it On the amnestic modification of the category of state property systems}, Appl. Categ. Struct., {\bf 10}\textbf{(5)} (2002), 469-480.
\bibitem{Birkhoff1935}
G.~Birkhoff, {\it On the structure of abstract algebras}, Proc. Cambridge Phil. Soc., {\bf 31} (1935), 433-454.
\bibitem{Chang1968}
C.~L. Chang, {\it Fuzzy topological spaces}, J. Math. Anal. Appl.,
{\bf 24} (1968), 182-190.
\bibitem{Cohn1981}
P.~M. Cohn, {\it Universal algebra}, D. Reidel Publ. Comp., 1981.
\bibitem{Demirci2010}
M.~Demirci, {\it Pointed semi-quantales and lattice-valued topological spaces}, Fuzzy Sets and Systems, {\bf 161}\textbf{(9)} (2010), 1224-1241.
\bibitem{Denniston2009}
J.~T. Denniston, A.~Melton and S.~E. Rodabaugh, {\it Lattice-valued topological systems}, In: U.~Bodenhofer, B.~De~Baets, E.~P. Klement, S.~Saminger-Platz, eds., Abstracts of the 30th Linz Seminar on Fuzzy Set Theory, Johannes Kepler Universit\"{a}t, Linz, (2009), 24-31.
\bibitem{Denniston2009a}
J.~T. Denniston and S.~E. Rodabaugh, {\it Functorial relationships between
lattice-valued topology and topological systems}, Quaest. Math.,
{\bf 32}\textbf{(2)} (2009), 139-186.
\bibitem{Dikranjan1988}
D.~Dikranjan, E.~Giuli and A.~Toi, {\it Topological categories and closure operators}, Quaest. Math., {\bf 11}\textbf{(3)} (1988), 323-337.
\bibitem{Eklund1986}
P.~Eklund, {\it Categorical fuzzy topology}, Ph.D. Thesis, \r{A}bo Akademi, 1986.
\bibitem{Gahler1992}
W.~G\"ahler, {\it Monadic topology-a new concept of generalized topology}, In: W.~G\"ahler, eds., Recent Developments of General Topology and Its Applications, Akademie-Verlag, Berlin, (1992), 136-149.
\bibitem{Goguen1973}
J.~A.~Goguen, {\it The fuzzy Tychonoff theorem}, J. Math. Anal. Appl.,
{\bf 43} (1973), 734-742.
\bibitem{Guido2010}
C.~Guido, {\it Fuzzy points and attachment}, Fuzzy Sets and Systems,
{\bf 161}\textbf{(16)} (2010), 2150-2165.
\bibitem{Guido2003}
C.~Guido, {\it Powerset operators based approach to fuzzy topologies on fuzzy sets}, In: S.~E. Rodabaugh, E.~P. Klement, eds., Topological and Algebraic Structures in Fuzzy Sets, Kluwer Academic Publishers, (2003), 401-413.
\bibitem{Guido2011}
C.~Guido and V.~Scarciglia, {\it $L$-topological spaces as spaces of points}, Fuzzy Sets and Systems, {\bf173(1)} (2011), 45-59.
\bibitem{Hohle1999a}
U.~H\"{o}hle and A.~P. \v{S}ostak, {\it Axiomatic foundations of fixed-basis fuzzy topology}, In: U.~H\"{o}hle, S.~E. Rodabaugh, eds., Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, Kluwer Academic Publishers, (1999), 123-272.
\bibitem{Hutton1980}
B.~Hutton, {\it Products of fuzzy topological spaces}, Topology Appl.,
{\bf 11} (1980), 59-67.
\bibitem{Isbell1972}
J.~R. Isbell, {\it Atomless parts of spaces}, Math. Scand.,
{\bf 31} (1972), 5-32.
\bibitem{John2008}
J.~John and T.~Baiju, {\it Metacompactness in $L$-topological spaces},
Iranian Journal of Fuzzy Systems, {\bf 5}\textbf{(3)} (2008), 71-79.
\bibitem{Johnstone1982}
P.~T. Johnstone, {\it Stone spaces}, Cambridge University Press, 1982.
\bibitem{Kelley1975}
J.~L. Kelley, {\it General topology}, Springer, 1975.
\bibitem{Kruml2008}
D.~Kruml and J.~Paseka, {\it Algebraic and categorical aspects of quantales}, In: M.~Hazewinkel, eds., Handbook of Algebra, Elsevier, {\bf5} (2008), 323-362.
\bibitem{Li2005}
S. P. Li, Z.~Fang and J.~Zhao, \emph{{P2-connectedness in $L$-topological spaces}}, Iranian Journal of Fuzzy Systems,
{\bf 2}\textbf{(1)} (2005), 29-36.
\bibitem{Lowen1976}
R.~Lowen, {\it Fuzzy topological spaces and fuzzy compactness}, J. Math. Anal. Appl., {\bf 56} (1976), 621-633.
\bibitem{MacLane1998}
S.~{Mac Lane}, {\it Categories for the working mathematician}, 2nd ed.,
Springer-Verlag, 1998.
\bibitem{Manes1976}
E.~G. Manes, {\it Algebraic theories}, Springer-Verlag, 1976.
\bibitem{Papert1959}
D.~Papert and S.~Papert, {\it Sur les treillis des ouverts et les paratopologies}, Semin. de Topologie et de Geometrie differentielle Ch. Ehresmann 1 (1957/58), {\bf 1} (1959), 1-9.
\bibitem{Pratt1999}
V.~Pratt, {\it Chu spaces}, Coimbra: Universidade de Coimbra, Departamento de Matem\'atica, Textos Mat., S\'er., {\bf B}\textbf{(21)} (1999), 39-100.
\bibitem{Pultr2003b}
A.~Pultr, {\it Frames}, In: M.~Hazewinkel, eds., Handbook of Algebra, North-Holland Elsevier, {\bf3} (2003), 789-858.
\bibitem{Pultr2003}
A.~Pultr and S.~E. Rodabaugh, {\it Lattice-valued frames, functor categories, and classes of sober spaces}, In: S.~E. Rodabaugh,
E.~P. Klement, eds., Topological and Algebraic Structures in Fuzzy Sets, Kluwer Academic Publishers, (2003), 153-187.
\bibitem{Pultr2008}
A.~Pultr and S.~E. Rodabaugh, {\it Category theoretic aspects of chain-valued frames: part I: categorical foundations}, Fuzzy Sets and Systems, {\bf 159}\textbf{(5)} (2008), 501-528.
\bibitem{Pultr2008a}
A.~Pultr and S.~E. Rodabaugh, {\it Category theoretic aspects of chain-valued frames: part II: applications to lattice-valued topology}, Fuzzy Sets and Systems, {\bf 159}\textbf{(5)} (2008), 529-558.
\bibitem{Rodabaugh1983}
S.~E. Rodabaugh, {\it A categorical accommodation of various notions of fuzzy topology}, Fuzzy Sets and Systems, {\bf 9} (1983), 241-265.
\bibitem{Rodabaugh1997}
S.~E. Rodabaugh, {\it Powerset operator based foundation for point-set
lattice-theoretic (poslat) fuzzy set theories and topologies}, Quaest. Math., {\bf 20}\textbf{(3)} (1997), 463-530.
\bibitem{Rodabaugh1999a}
S.~E. Rodabaugh, {\it Categorical foundations of variable-basis fuzzy topology}, In: U.~H\"{o}hle, S.~E. Rodabaugh, eds., Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, Kluwer Academic Publishers, (1999), 273-388.
\bibitem{Rodabaugh1999c}
S.~E. Rodabaugh, {\it Powerset operator foundations for poslat fuzzy set theories and topologies}, In: U.~H\"{o}hle, S.~E. Rodabaugh, eds., Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, Kluwer Academic Publishers, (1999), 91-116.
\bibitem{Rodabaugh2007}
S.~E. Rodabaugh, {\it Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics}, Int. J. Math. Math. Sci., {\bf 2007} (2007), 1-71.
\bibitem{Rosenthal1990}
K.~I. Rosenthal, {\it Quantales and their applications}, Addison Wesley Longman, 1990.
\bibitem{Shi2004}
F. G. Shi, {\it Countable compactness and the Lindel\"{o}f property of $L$-fuzzy sets}, Iranian Journal of Fuzzy Systems, {\bf 1}\textbf{(1)} (2004), 79-88.
\bibitem{Shi2010}
F. G. Shi and P. Chen, {\it The Urysohn axiom and the completely Hausdorff axiom in $L$-topological spaces}, Iranian Journal of Fuzzy Systems,
{\bf 7}\textbf{(1)} (2010), 33-45.
\bibitem{Shostak1989}
A.~P.~Shostak, {\it Two decades of fuzzy topology: basic ideas, notions, and results}, Russ. Math. Surv., {\bf 44}\textbf{(6)} (1989), 125-186.
\bibitem{Solovjovs2008a}
S.~Solovjovs, {\it On a categorical generalization of the concept of fuzzy set: basic definitions, properties, examples}, VDM Verlag Dr. M\"{u}ller, 2008.
\bibitem{Solovjovs2009}
S.~Solovjovs, {\it Embedding topology into algebra}, In: U.~Bodenhofer, B.~De~Baets, E.~P. Klement, S.~Saminger-Platz, eds., Abstracts of the 30th Linz Seminar on Fuzzy Set Theory, Johannes Kepler Universit\"{a}t, Linz, (2009), 106-110.
\bibitem{Solovyov2010c}
S.~Solovyov, {\it Localification of variable-basis topological systems}, Quaest. Math., {\bf34(1)} (2011), 11-33.
\bibitem{Solovyovl}
S.~Solovyov, {\it On a generalization of the concept of state property system}, Soft Comput., to appear.
\bibitem{Solovyovq}
S.~Solovyov, {\it Powerset operator foundations for catalg fuzzy set theories}, Iranian Journal of Fuzzy Systems, {\bf 8(2)} (2011), 1-46.
\bibitem{Solovyov2008d}
S.~Solovyov, {\it Categorical frameworks for variable-basis sobriety and spatiality}, Math. Stud. Tartu, {\bf 4} (2008), 89-103.
\bibitem{Solovyov2008b}
S.~Solovyov, {\it Sobriety and spatiality in varieties of algebras}, Fuzzy Sets and Systems, {\bf 159}\textbf{(19)} (2008), 2567-2585.
\bibitem{Solovyov2010a}
S.~Solovyov, {\it Variable-basis topological systems versus variable-basis topological spaces}, Soft Comput.,
{\bf 14}\textbf{(10)} (2010), 1059-1068.
\bibitem{Vickers1989}
S.~Vickers, {\it Topology via logic}, Cambridge University Press, 1989.
\bibitem{Vickers1993}
S.~Vickers, {\it Information systems for continuous posets}, Theor. Comput. Sci., {\bf 114}\textbf{(2)} (1993), 201-229.
\bibitem{Wen2008}
G. F. Wen, F. G. Shi and H. Y. Li, {\it Almost $S^*$-compactness in
$L$-topological spaces}, Iranian Journal of Fuzzy Systems,
{\bf 5}\textbf{(3)} (2008), 31-44.
\bibitem{Zadeh1965}
L.~A. Zadeh, {\it Fuzzy sets}, Information and Control, {\bf 8} (1965), 338-365.
)