Topological aspects of non-convergent sequences - A comment on Burgin's concept of fuzzy limits

Fuzzy Sets and Systems

Volumn 149, Issue 3, 2005, Pages 399-412

  Höhle, Ulrich ^a  

^a UNIVERSITY OF WUPPERTAL   (Germany)

Author keywords

Limit maps; Limit points; Topology on a 0, 1 valued set

Indexed keywords

COMPUTATIONAL GEOMETRY; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL OPERATORS; SET THEORY; TOPOLOGY;

LIMIT MAPS; LIMIT POINTS; REAL NUMBERS; TOPOLOGY ON A [0,1]-VALUED SET;

FUZZY SETS;

EID: 10444252712     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2004.06.001     Document Type: Article

References (19)

1. M. Burgin, Neoclassical analysis: fuzzy continuity and convergence, Fuzzy Sets and Systems 75 (1995) 291-299.
2. M. Burgin, General approach to continuity measures, Fuzzy Sets and Systems 105 (1999) 225-231.
3. M. Burgin, Theory of fuzzy limits, Fuzzy Sets and Systems 115 (2000) 433-443.
4. C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968) 182-190.
5. M. Fourman, D.S. Scott, Sheaves and logic, Applications of Sheaves: Lecture Notes in Mathematics, vol. 753, Springer, Berlin, New York, 1979, pp. 302-401.
6. M. Fréchet, Sur divers modes de convergence d'une suite de fonctions d'une variable, Bull. Calcutta Math. Soc. 11 (1921) 187-206.
7. O. Frink, New algebras of logic, Amer. Math. Assoc. Monthly 45 (1938) 210-219.
8. U. Höhle, M-valued sets and sheaves over integral commutative cl-monoids, in: S.E. Rodabaugh, et al. (Eds.), Applications of Category Theory to Fuzzy Subsets, Kluwer Academic Publishers, Dordrecht, Boston, London, 1992, pp. 33-72.
9. U. Höhle, Commutative, residuated ℓ-monoids, in: U. Höhle, E.P. Klement (Eds.), Nonclassical Logics and their Applications to Fuzzy Subsets, Kluwer Academic Publishers, Dordrecht, Boston, 1995, pp. 53-106.
10. U. Höhle, Presheaves over GL-monoids, in: U. Höhle, E.P. Klement (Eds.), Non-classical Logics and their Applications to Fuzzy Subsets, Kluwer Academic Publishers, Dordrecht, Boston, 1995, pp. 127-157.
11. U. Höhle, Many-valued equalities, singletons and fuzzy partitions, Soft Comput. 2 (1998) 134-140.
12. U. Höhle, Classification of subsheaves over GL-algebras, in: S.R. Buss, et al. (Eds.), Logic Coll. '98, Lecture Notes in Logic, vol. 13, Association for Symbolic Logic, 2000, pp. 238-261.
13. U. Höhle, Conuclei and many valued topology, Acta Math. Hungar. 88 (2000) 259-267.
14. U. Höhle, Limit structures and many valued topological spaces, J. Math. Anal. Appl. 251 (2000) 549-556.
15. U. Höhle, Many Valued Topology and its Applications, Kluwer Academic Publishers, Boston, Dordrecht, 2001.
16. U. Höhle, Many valued equalities and their representations, in: R. Mesiar, E.P. Klement (Eds.), Triangular Norms and Related Operators, Kluwer Academic Publishers, Dordrecht, forthcoming.
17. U. Höhle, A.P. Šostak, Axiomatic foundations of fixed-basis fuzzy topology, in: U. Höhle, S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets, Kluwer Academic Publishers, Boston, Dordrecht, London, 1999, pp. 123-272.
18. P.T. Johnstone, Stone Spaces, Cambridge University Press, Cambridge, London, New York, 1982.
19. M. Kalina, Fuzzy smoothness and sequences of fuzzy smooth functions, Fuzzy Sets and Systems 105 (1999) 233-239.