On φ 1,2-countable compactness and filters

[EN] In this work the author investigates some relations between φ 1,2-countable compactness, filters, sequences and φ 1,2-closure operators.Yalvaç, T. (2003). On φ 1,2-countable compactness and filters. Applied General Topology. 4(1):35-46. doi:10.4995/agt.2003.2008.SWORD354641A. S. Mashhour, A. A. Allam, F. S. Mahmoud and F. H. Khedr, On supratopological spaces, Indian J. Pure Appl. Math. 14 (4) (1983), 502-510.M. E. Abd El-Monsef and E. F. Lashien, Local discrete extensions of supratopologies, Tamkong J. Math 31 (1) (1990), 1-6.R. F. Dickmann Jr. and J. R. Porter, θ-perfect and absolutely closed functions, Illinois J. Math. 21 (1977), 42-60.Dickman, R. F., & Krystock, R. L. (1980). S-Sets and S-Perfect Mappings. Proceedings of the American Mathematical Society, 80(4), 687. doi:10.2307/2043452G. Di Maio and T. Noiri, On s-closed spaces, Indian J. Pure Appl. Math. 18 (3) (1987), 226-233.K. Dlaska, N. Ergun and M. Ganster, Countably S-closed spaces, Math. Slovaca 44 (3) (1994), 337-348.J. Dontchev and M. Ganster, On covering spaces with semi-regular sets, Ricerche Math. 45 (1996), 229-245.J. Dugundji, Topology, (Allyn and Bacon, Boston, Mass., 1966).Herrmann, R. A. (1979). rc-convergence. Proceedings of the American Mathematical Society, 75(2), 311-311. doi:10.1090/s0002-9939-1979-0532157-5Herrington, L. L., & Long, P. E. (1975). Characterizations of H-Closed Spaces. Proceedings of the American Mathematical Society, 48(2), 469. doi:10.2307/2040285Herrington, L. L. (1976). Remarks on H(i) Spaces and Strongly-Closed Graphs. Proceedings of the American Mathematical Society, 58(1), 277. doi:10.2307/2041400A. Kandil, E. E. Kerre and A. A. Nouh,Operations and mappings on fuzzy topological spaces, Ann. Soc. Sci. Bruxelles 105 (4) (1991), 165-168.S. N. Maheshwari and S. S. Thakur, Jour. Sci. Res. 3 (1981), 121-123.S. N. Maheshwari and S. S. Thakur, On α-compact spaces, Bull. Inst. Math. Academia Sinica 13 (4) (1985), 341-347.T. Noiri, On RS-compact spaces, J. Korean Math. Soc. 22 (1) (1985), 19-34.T. G. Raghavan, On H(1)-closed spaces-II, Bull. Cal. Math. Soc. 77 (1985), 171-180.Stephenson, R. M. (1968). Pseudocompact spaces. Transactions of the American Mathematical Society, 134(3), 437-437. doi:10.1090/s0002-9947-1968-0232349-6T. Thompson, SQ-closed spaces, Math. Japonica 22 (4) (1977), 491-495.D. Thanapalan and T. G. Raghavan, On strongly H(1)-closed spaces, Bull. Cal. Math. Soc. 76 (1984), 370-383.T. H. Yalvaç, A unified approach to compactness and filters, Hacettepe Bull. Nat. Sci. Eng., Series B 29 (2000), 63-75.T. H. Yalvaç, On some unifications (Presented at The First Turkish International Conference on Topology and Its Applications, Istanbul, 2000), Hacettepe Bull. Nat. Sci. Eng., Series B 30 (2001), 27-38.T. H. Yalvaç, A unified theory on some basic topological concepts, International Conference on Topology and its Applications, Macedonia, (2000). T. H. Yalvaç, Unifications of some concepts related to the Lindelöf property, submitted

Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results

[EN] With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see "Am. Math. Month. 1967, 74, 436-437") that a metric space is complete if and only if any Banach contraction on any of its closed subsets has a fixed point. We apply our main result to deduce that a well-known fixed point theorem due to D. Mihet (see "Fixed Point Theory 2005, 6, 71-78") also allows us to characterize the fuzzy metric completeness.This research was partially funded by Ministerio de Ciencia, Innovacion y Universidades, under grant PGC2018-095709-B-C21 and AEI/FEDER, UE funds.Romaguera Bonilla, S.; Tirado Peláez, P. (2020). Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results. Mathematics. 8(2):1-7. https://doi.org/10.3390/math8020273S1782Connell, E. H. (1959). Properties of fixed point spaces. Proceedings of the American Mathematical Society, 10(6), 974-979. doi:10.1090/s0002-9939-1959-0110093-3Hu, T. K. (1967). On a Fixed-Point Theorem for Metric Spaces. The American Mathematical Monthly, 74(4), 436. doi:10.2307/2314587Subrahmanyam, P. V. (1975). Completeness and fixed-points. Monatshefte f�r Mathematik, 80(4), 325-330. doi:10.1007/bf01472580Kirk, W. A. (1976). Caristi’s fixed point theorem and metric convexity. Colloquium Mathematicum, 36(1), 81-86. doi:10.4064/cm-36-1-81-86Caristi, J. (1976). Fixed point theorems for mappings satisfying inwardness conditions. Transactions of the American Mathematical Society, 215, 241-241. doi:10.1090/s0002-9947-1976-0394329-4Suzuki, T., & Takahashi, W. (1996). Fixed point theorems and characterizations of metric completeness. Topological Methods in Nonlinear Analysis, 8(2), 371. doi:10.12775/tmna.1996.040Suzuki, T. (2007). A generalized Banach contraction principle that characterizes metric completeness. Proceedings of the American Mathematical Society, 136(05), 1861-1870. doi:10.1090/s0002-9939-07-09055-7Romaguera, S., & Tirado, P. (2019). A Characterization of Quasi-Metric Completeness in Terms of α–ψ-Contractive Mappings Having Fixed Points. Mathematics, 8(1), 16. doi:10.3390/math8010016Samet, B., Vetro, C., & Vetro, P. (2012). Fixed point theorems for -contractive type mappings. Nonlinear Analysis: Theory, Methods & Applications, 75(4), 2154-2165. doi:10.1016/j.na.2011.10.014Abbas, M., Ali, B., & Romaguera, S. (2015). Multivalued Caristi’s type mappings in fuzzy metric spaces and a characterization of fuzzy metric completeness. Filomat, 29(6), 1217-1222. doi:10.2298/fil1506217aCastro-Company, F., Romaguera, S., & Tirado, P. (2015). On the construction of metrics from fuzzy metrics and its application to the fixed point theory of multivalued mappings. Fixed Point Theory and Applications, 2015(1). doi:10.1186/s13663-015-0476-1Radu, V. (1987). Some fixed point theorems probabilistic metric spaces. Lecture Notes in Mathematics, 125-133. doi:10.1007/bfb0072718Sehgal, V. M., & Bharucha-Reid, A. T. (1972). Fixed points of contraction mappings on probabilistic metric spaces. Mathematical Systems Theory, 6(1-2), 97-102. doi:10.1007/bf01706080Ćirić, L. (2010). Solving the Banach fixed point principle for nonlinear contractions in probabilistic metric spaces. Nonlinear Analysis: Theory, Methods & Applications, 72(3-4), 2009-2018. doi:10.1016/j.na.2009.10.00

On topological structures of fuzzy parametrized soft sets

In this paper, we introduce the topological structure of fuzzy parametrized soft sets and fuzzy parametrized soft mappings. We define the notion of quasi-coincidence for fuzzy parametrized soft sets and investigated basic properties of it. We study the closure, interior, base, continuity and compactness and properties of these concepts in fuzzy parametrized soft topological space