Fuzzification of strongly and locally strongly compact spaces
DOI:
https://doi.org/10.22199/issn.0717-6279-4948Keywords:
Lukasiewicz logic, semantics, fuzzifying topology, fuzzifying compactness, strong compactness, fuzzifying locally compactness, locally strong compactnessAbstract
In this paper, some characterizations of fuzzifying strong compact- ness are given, including characterizations in terms of nets and pre- subbases. Several characterizations of locally strong compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.
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S. A. Abd El-Baki and O. R. Sayed, Pre-irresolutness and strong compactness in fuzzifying topology, Journal of the egyptian mathematical society, vol. 15 (1), pp. 41-56, 2007. [On line]. Available: https://bit.ly/3r1j9UR
K. M. Abd El-Hakeim, F. M. Zeyada, and O. R. Sayed, “Pre-Continuity and D(c,p)-continuity in fuzzifying topology”, Fuzzy sets and systems, vol. 119, no. 3, pp. 459–471, 2001. https://doi.org/10.1016/s0165-0114(99)00097-4
K. M. Abd El-Hakeim, F. M. Zeyada and O. R. Sayed, “Pre-separation axioms in fuzzifying topology, Fuzzy systems and mathematics, vol. 17, pp. 29-37, 2003.
C. L. Chang, “Fuzzy topological spaces”, Journal of mathematical analysis and applications, vol. 24, pp. 182-190, 1968. [On line]. Available: https://bit.ly/31GClOX
A. Dutta and B. C. Tripathy, “On fuzzy b-θ open sets in fuzzy topological space”, Journal of intelligent & fuzzy systems, vol. 32, no. 1, pp. 137–139, 2017. https://doi.org/10.3233/jifs-151233
J. A. Goguen, “The fuzzy tychonoff theorem”, Journal of mathematical analysis and applications, vol. 43, no. 3, pp. 734–742, 1973. https://doi.org/10.1016/0022-247x(73)90288-6
U. Höhle, “Upper semicontinuous fuzzy sets and applications”, Journal of mathematical analysis and applications, vol. 78, no. 2, pp. 659–673, 1980. https://doi.org/10.1016/0022-247x(80)90173-0
U. Höhle, Many valued topology and its applications. Dordrecht: Kluwer Academic Publishers, 2001.
U. Höhle and S. E. Rodabaugh, Mathematics of fuzzy sets: logic, topology, and measure theory. Dordrecht: Kluwer Academic Publishers, 1999. https://doi.org/10.1007/978-1-4615-5079-2
U. Höhle, S. E. Rodabaugh, and A. Sostak, (Eds.), Fuzzy Topology. Elsevier, 1995. https://bit.ly/3rJ3sSB
Höhle U and A. Šostak, “Axiomatic foundations of fixed-basis fuzzy topology,” in Mathematics of fuzzy sets: logic, topology, and measure theory, Höhle U and S. E. Rodabaugh, Eds. Dordrecht: Kluwer Academic Publishers, 1999, pp. 123–272. https://doi.org/10.1007/978-1-4615-5079-2_5
J. L. Kelley, General Topology. New York: Van Nostrand, 1955.
Kubiak, T., 1985. On fuzzy topologies. Ph.D. Thesis. Adam Mickiewicz University, Poznan, Poland.
Y. M. Liu and M. K. Luo, Fuzzy topology. Singapore: World Scientific, 1998.
A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, “On precontinuous and weak pre-continuous mappings”, Proceedings of the mathematical and physical society of Egypt, vol. 53, pp. 255-263, 1982.
A. S. Mashhour, M. E. Abd El-Monsef, I. A. Hasanein and T. Noiri, “Strongly compact spaces”, Delta journal of science, vol. 8, pp. 30-64, 1984.
D. Qiu, “Fuzzifying topological linear spaces”, Fuzzy sets and systems, vol. 147, no. 2, pp. 249–272, 2004. https://doi.org/10.1016/j.fss.2003.10.024
D. Qiu, “Characterizations of fuzzy finite automata”, Fuzzy sets and systems, vol. 141, no. 3, pp. 391–414, 2004. https://doi.org/10.1016/s0165-0114(03)00202-1
G. C. Ray and B. C. Tripathy, “Fuzzy δ∗-almost continuous and fuzzy δ∗-continuous functions in mixed fuzzy ideal topological spaces”, Proyecciones (Antofagasta), vol. 39, no. 2, pp. 435–449, 2020. https://doi.org/10.22199/issn.0717-6279-2020-02-0027
S. E. Rodabaugh, “Categorical foundations of variable-basis fuzzy topology”, in Mathematics of fuzzy sets: logic, topology, and measure theory, Höhle U and S. E. Rodabaugh, Eds. Dordrecht: Kluwer Academic Publishers, 1999, pp. 273-388. https://doi.org/10.1007/978-1-4615-5079-2_6
J. B. Rosser and A. R. Turquette, Many-valued logics. Amsterdam: North-Holland, 1952.
D. J. Sarma and B. C. Tripathy, “Fuzzy semi-pre quasi neighborhood structure”, Afrika matematika, vol. 30, no. 1-2, pp. 217–221, 2019. https://doi.org/10.1007/s13370-018-0637-6
O. R. Sayed, On fuzzifying topological spaces. Ph.D. Thesis. Assiut University, Egypt, 2002.
J. Shen, “Locally compactness in fuzzifying topology”, Journal of fuzzy mathematics, vol. 2, no. 4, pp. 695-711, 1994.
B. C. Tripathy and G. C. Ray, “Mixed fuzzy ideal topological spaces”, Applied mathematics and computation, vol. 220, pp. 602–607, 2013. https://doi.org/10.1016/j.amc.2013.05.072
B. C. Tripathy and G. C. Ray, “On δ-continuity in mixed fuzzy topological spaces”, Boletim da sociedade paranaense de matemática, vol. 32, no. 2, pp. 175–187, 2014. https://doi.org/10.5269/bspm.v32i2.20254
B. C. Tripathy and G. C. Ray, “Weakly continuous functions on mixed fuzzy topological spaces”, Acta scientiarum. technology, vol. 36, no. 2, pp. 331–335, 2014. https://doi.org/10.4025/actascitechnol.v36i2.16241
B. C. Tripathy and G. C. Ray, “Fuzzy δ-I -continuity in mixed fuzzy ideal topological spaces”, Journal of applied analysis, vol. 24, no. 2, pp. 233–239, 2018. https://doi.org/10.1515/jaa-2018-0022
G. J. Wang, Theory of L-fuzzy topological spaces ,Xi’an: Shanxi Normal University Press, 1988. (in Chinese),
M. S. Ying, “A new approach for fuzzy topology (I)”, Fuzzy sets and systems, vol. 39, no. 3, pp. 303–321, 1991. https://doi.org/10.1016/0165-0114(91)90100-5
M. S. Ying, “A new approach for fuzzy topology (II)”, Fuzzy sets and systems, vol. 47, no. 2, pp. 221–232, 1992.https://doi.org/10.1016/0165-0114(92)90181-3
M. S. Ying, “A new approach for fuzzy topology (III)”, Fuzzy sets and systems, vol. 55, no. 2, pp. 193–207, 1993. https://doi.org/10.1016/0165-0114(93)90132-2
M. S. Ying, “Compactness in fuzzifying topology”, Fuzzy sets and systems, vol. 55, no. 1, pp. 79–92, 1993. https://doi.org/10.1016/0165-0114(93)90303-y
M. S. Ying, “Fuzzifying topology based on complete residuated lattice-valued logic (I)”, Fuzzy sets and systems, vol. 56, no. 3, pp. 337–373, 1993. https://doi.org/10.1016/0165-0114(93)90215-4
M. S. Ying, “Fuzzy topology based on residuated lattice-valued logic,” Acta mathematica sinica, English series, vol. 17, no. 1, pp. 89–102, 2001. https://doi.org/10.1007/s101140000079
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