We came up with the concept ππ * -open set which has stricter condition with respect to the notion b-open sets, introduced by Andrijevic as a generalization of Levineβs generalized closed sets. Anchoring on this concept, we defined ππ πΌπΌ * * -hyperconnected sets and ππ * -separated sets. Topology is seen in many areas of science, for example, it is used to model the spacetime notion of the universe. It is sometimes investigated in non-conventional ways, for example Donaldson utilized mathematical concepts used by physicists to solve topological problems. These problems includes new topological sets like ππ * -open set.
We came up with the concept Γ°ΒβΖΓ°ΒβΖΓ’Λβ-open set which has stricter condition with respect to the notion b-open sets, introduced by Andrijevic [3] as a generalization of Levine's [11] generalized closed sets. Anchoring on this concept, we defined Γ°ΒβΖΓ°ΒβΖΓ°Ββ°ðΒβΒ° Γ’ΛβΓ’Λβ-hyperconnected sets and Γ°ΒβΖΓ°ΒβΖΓ’Λβ -separated sets. Topology is seen in many areas of science, for example, it is used to model the space-time notion of the universe. It is sometimes investigated in non-conventional ways, for example Donaldson [7] utilized mathematical concepts used by physicists to solve topological problems. These problems includes new topological sets like Γ°ΒβΖΓ°ΒβΖΓ’Λβ-open set. A subset B of a topological space W is called a Γ°ΒβΖΓ°ΒβΖΓ’Λβ-open relative to an ideal I (or -open), if there is an open set P with , and a closed set S with such that In this study, we gave some of the important properties of Γ°ΒβΖΓ°ΒβΖΓ°Ββ°ðΒβΒ° Γ’ΛβΓ’Λβ-hyperconnected sets and Γ°ΒβΖΓ°ΒβΖΓ’Λβ-separated sets.