Exploring Hyperconnectedness and Separation in Ideal Topological Spaces
We came up with the concept 𝒃𝒃∗-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 𝒃𝒃𝑰𝑰 ∗∗-hyperconnected sets and 𝒃𝒃∗ -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 𝒃𝒃∗-open set. A subset B of a topological space W is called a 𝒃𝒃∗-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 𝒃𝒃𝑰𝑰 ∗∗-hyperconnected sets and 𝒃𝒃∗-separated sets.
