Characterizations of Some Topological Spaces (European Journal of Pure and Applied Mathematics, 2023)
This paper is concerned with the concepts of some topological spaces. Firstly, we introduce the notions of δs(Λ, p)-open sets. Some properties concerning δs(Λ, p)-open sets are discussed. Secondly, the concept of s(Λ, p)-connected spaces is introduced. Moreover, we give several characterizations of s(Λ, p)-connected spaces by utilizing δs(Λ, p)-open sets. Thirdly, we apply the notion of s(Λ, p)-open sets to present and study new classes of spaces called s(Λ, p)-regular spaces and s(Λ, p)-normal spaces. Especially, some characterizations of s(Λ, p)-regular spaces and s(Λ, p)-normal spaces are established. Fourthly, we introduce and investigate the concepts of s(Λ, p)-T2 spaces and s(Λ, p)-Urysohn spaces. Finally, the notion of S(Λ, p)-closed spaces is studied. Basic properties and characterizations of S(Λ, p)-closed spaces are considered.
Keywords: $δ s(Λ,p)$-open set; $s(Λ,p)$-connected space; $s(Λ,s)$-regular space; $s(Λ,s)$-normal space; $s(Λ,p)$-$T_2$ space; $s(Λ,p)$-Urysohn space; $S(Λ,p)$-closed space