Abstract
The objective of this work is to study some topological properties of partial fuzzy metric spaces. For this purpose, we first define a topology generated by the partial fuzzy metric in the sense of Sedghi et al. [8] We give some relationships between the topologies induced by partial metric and partial fuzzy metric. Then, we investigate various properties including countability, completeness and separation axioms and we give Baire’s theorem for partial fuzzy metric spaces. Finally, we obtain that partial fuzzy metric topological spaces are metrizable under some assumptions.
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References
Bukatin, M., Kopperman, R., Matthews, S., Pajoohesh, H.: Partial metric space. Am. Math. Monthly 116(8), 708–718 (2009)
George, A., Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64(3), 395–399 (1994)
Gregori, V., Minana, J.J., Miravet, D.: Fuzzy partial metric spaces. Int. J. Gen. Syst. 48(3), 260–279 (2019)
Gregori, V., Romaguera, S.: Some properties of fuzzy metric spaces. Fuzzy Sets Syst. 115(3), 485–489 (2000)
Matthews, S.: Partial metric topology. Ann. N. Y. Acad. Sci. 728, 183–197 (1994)
Piera, A.S.: A contribution to the study of fuzzy metric spaces. Appl. Gen. Topology 2(1), 63–75 (2001)
Rodriguez-López, J., Romaguera, S.: The Hausdorff fuzzy metric on compact sets. Fuzzy Sets Syst. 147(2), 273–283 (2004)
Sedghi, S., Shobkolaei, N., Altun, I.: Partial fuzzy metric space and some fixed point results. Commun. Math. 23(2), 131–142 (2015)
Yue, Y., Gu, M.: Fuzzy partial (pseudo-) metric space. J. Intell. Fuzzy Syst. 27(3), 1153–1159 (2014)
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Aydogdu, E., Aldemir, B., Güner, E., Aygün, H. (2021). Some Properties of Partial Fuzzy Metric Topology. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I., Cebi, S., Tolga, A. (eds) Intelligent and Fuzzy Techniques: Smart and Innovative Solutions. INFUS 2020. Advances in Intelligent Systems and Computing, vol 1197. Springer, Cham. https://doi.org/10.1007/978-3-030-51156-2_148
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DOI: https://doi.org/10.1007/978-3-030-51156-2_148
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