Extremal Fuzzy Space
Keywords:
an extremal topology; Fuzzy space; ultrafilter; door space
Abstract
The extremal topology on an arbitrary set X was defined as a maximal non-discrete topology [1] and [2]. In this paper we introduce an extremal topology on a fuzzy set X, which is also a maximal non-discrete topology, and it has to be in a specific form. This form depends on some ultrafilters = . We consider some properties for this kind of topologies when = is free. The subspaces and the base of this topology is also considered.
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References
[1] Papazyan, T. Extremal topologies on a semigroup, Topology and its applications 39 (1991) 229-243
[2] Mera, K. M. and Sola, M. A. ( 2005) Extremal Topology, Damascus University Journal for basic science, vol.21, No1.
[3] Sola, M. A. A note on extremal topologies, unpublished paper.
[4] Kelley, John L. General Topology. Springer. ISBN 3540901256. (1991).
[5] Willard, S. (1970). General Topology, Addision-Wesley Publishing Company, INC
[6] Zadeh, L. A. (1965), Fuzzy Sets, Information and Control, 8, pp. 338-353.
[7] Chang, C. L. (1968), Fuzzy topological spaces, J. Math. Anal. Appl., 24, pp. 182-190.
[8] M. A. Vicente AND M. S. Aranguren, ”Fuzzy Filters”, journal of Mathematical analysis and applications 129, 56G-568 (1988)
[9] Zadeh, L. A., A Fuzzy-Set-Theoretic Interpretation of Linguistic Hedges, ERL Memorandum M335, University of California, Berkeley, April (1972). (To appear in Information Sciences.)
[10] Wong, C. K., Fuzzy topology: Product and quotient theorems, J. Math. Anal. Appl. 45 (1974), 512-521.
[11] C. De Mitri and E. Pascali, On Sequential Compactness and Semicompactness in Fuzzy Topology, journal of Mathematical analysis and applications 93. 324-327 (1983)
[2] Mera, K. M. and Sola, M. A. ( 2005) Extremal Topology, Damascus University Journal for basic science, vol.21, No1.
[3] Sola, M. A. A note on extremal topologies, unpublished paper.
[4] Kelley, John L. General Topology. Springer. ISBN 3540901256. (1991).
[5] Willard, S. (1970). General Topology, Addision-Wesley Publishing Company, INC
[6] Zadeh, L. A. (1965), Fuzzy Sets, Information and Control, 8, pp. 338-353.
[7] Chang, C. L. (1968), Fuzzy topological spaces, J. Math. Anal. Appl., 24, pp. 182-190.
[8] M. A. Vicente AND M. S. Aranguren, ”Fuzzy Filters”, journal of Mathematical analysis and applications 129, 56G-568 (1988)
[9] Zadeh, L. A., A Fuzzy-Set-Theoretic Interpretation of Linguistic Hedges, ERL Memorandum M335, University of California, Berkeley, April (1972). (To appear in Information Sciences.)
[10] Wong, C. K., Fuzzy topology: Product and quotient theorems, J. Math. Anal. Appl. 45 (1974), 512-521.
[11] C. De Mitri and E. Pascali, On Sequential Compactness and Semicompactness in Fuzzy Topology, journal of Mathematical analysis and applications 93. 324-327 (1983)
Published
2021-05-17
How to Cite
Mira, K., & Abdeen, K. (2021). Extremal Fuzzy Space. Journal of Progressive Research in Mathematics, 18(2), 1-4. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/2046
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