Fuzzification of strongly and locally strongly compact spaces

Authors

  • Osama Sayed Assiut University.
  • Adem Kılı¸cman University Putra Malaysia.

DOI:

https://doi.org/10.22199/issn.0717-6279-4948

Keywords:

Lukasiewicz logic, semantics, fuzzifying topology, fuzzifying compactness, strong compactness, fuzzifying locally compactness, locally strong compactness

Abstract

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.

Author Biographies

Osama Sayed, Assiut University.

Department of Mathematics, Faculty of Science.

Adem Kılı¸cman, University Putra Malaysia.

Department of Mathematics.

References

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

Published

2022-01-28

How to Cite

[1]
O. Sayed and A. Kılı¸cman, “Fuzzification of strongly and locally strongly compact spaces”, Proyecciones (Antofagasta, On line), vol. 41, no. 1, pp. 45-82, Jan. 2022.

Issue

Section

Artículos