7d6c6b13-c3bd-44c6-87c3-64ae8939b7a520210218104402089wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS1109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40512720202720201910.37394/23206.2020.19http://wseas.org/wseas/cms.action?id=23185(Λ, Sp)-closed Sets and Related Topics in Topological SpacesChawalitBoonpokMathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham, 44150, THAILANDThe purpose of the present paper is to introduce the concepts of Λsp-sets, (Λ, sp)-open sets and (Λ, sp)- closed sets which are defined by utilizing the notions of β-open sets and β-closed sets. Some characterizations of Λsp-submaximal spaces, Λsp-extremally disconnected spaces and Λsp-hyperconnected spaces are established. Moreover, several characterizations of upper and lower (Λ, sp)-continuous multifunctions are investigated.692020692020312322https://www.wseas.org/multimedia/journals/mathematics/2020/a625106-1231.pdf10.37394/23206.2020.19.31https://www.wseas.org/multimedia/journals/mathematics/2020/a625106-1231.pdfM.–E. Abd El-Monsef, S.–N. El-Deeb and R.–A. Mahmoud,β-open sets andβ-continuous mappings, Bull. Fac. Sci. Assiut Univ.12, 1983,pp. 77–90.10.1007/bf00051755N. Ajmal and J.–K. Kohli, Properties of hyperconnected spaces, their mappings into Haus-dorff spaces and embeddings into hypercon-nected spaces, Acta Math. Hungar.60, 1992,pp. 41–49.D. Andrijevi ́c, Onb-open sets,Mat. Vesnik48,1996, pp. 59–64.A.–V. Arhangelski ̆i and P.–J. Collins, On sub-maximal spaces,Topology Appl.64,1995,pp. 219–241.T. Banzaru, Multifunctions and M-productspaces,Bull.Stin.Tech.Inst.Politech.Timisoara, Ser. Mat. Fiz. Mer. Teor. Apl.17(31),1972, pp. 17–23.D. Cameron, Properties of S-closed spaces,Proc. Oklahoma Topology Conf., Oklahoma,1978.10.1016/0166-8641(93)90145-4E.–K. van Douwen, Applications of maximal topologies,Topology Appl.51, 1993, pp. 125–139. L. Gillman and M. Jerison, Rings of continuous functions, Univ. Series in Higher Math., Van Nostrand, Princeton, New York, 1960.J.–A. Guthrie, H.–E. Stone and M.–L. Wage, Maximal connected Hausdorff topologies, Topology Proc.2, 1977, pp. 349–353.[10] R.–A. Herrman, A nonstandard approach toS-spaces,Topology Proc.3, 1978, pp. 123–138.R.–A. Herrman,RC-convergence, Proc. Amer.Math. Soc.75, 1979, pp. 311–317.10.1215/s0012-7094-43-01029-4E. Hewitt, A problem of set-theoretic topology,Duke Math. J.10, 1943, pp. 309–333.N. Levine, Dense topologies,Amer. Math.Monthly75, 1968, pp. 847–852.10.2307/2312781N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly70,1963, pp. 36–41.T. Neubrunn, Strongly quasi-continuous multivalued mappings,General Topology and its Relations to Modern Analysis and AlgebraVI (Prague 1986) Heldermann, Berlin, 1988,pp. 351–359.10.1023/b:amhu.0000028409.42549.72T. Noiri and E. Hatir, Λsp-sets and some weak separation axions, Acta Math. Hungar.103,2004, pp. 225–232.[17] T. Noiri, Properties of hyper connected spaces, Acta Math. Hungar.66, 1995, pp. 147–154.10.1090/s0002-9939-1980-0565364-4T. Noiri, Characterizations of extremally disconnected spaces,Indian J. Pure Appl. Math.19,1988, pp. 325–329.[19] T. Noiri, A note on extremally disconnected spaces,Pro. Amer. Math. Soc.79(2), 1980,pp. 327–330.10.4171/rlmT. Noiri, On S-closed subspaces, Atti Accad.Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.64,1978, pp. 273–285.V. Popa and T. Noiri, Characterizations ofα-continuous multifunctions, Math. Slovaca43,1993, pp. 477–491.V. Popa and T. Noiri, On upper and lowerα-continuous multifunctions, Univ. u Novom SaduZb. Rad. Prirod.-Mat. Fak. Ser. Mat.23(1), 1993,pp. 29–38.A.–K. Sharma,Math. Vesnik.1(14)(29), 1977,pp. 25–27.D. Sivaraj, A note on extremally disconnected spaces,Indian J. Pure Appl. Math.17, 1986,pp. 1373–1375.L.–A. Steen and J.–A. Seebach, Jr., Counter examples in Topology, Holt, Rinehart and Winston,New York, 1970.T. Thompson, S-closed spaces, Proc. Amer.Math. Soc.60, 1976, pp. 335–338.