Local function versus local closure function in ideal topological spaces

Abstract

The aim of this paper is to further investigate properties of the local closure function, as a generalization of the ?-closure and the local function in ideal topological spaces. Similarities and differences between it and the local function are examined by varying several well-known ideals. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 174006]

New topologies from obtained operators via weak semi-local function and some comparisons

“…In [1], a question was asked that "Is there an example that shows σ σ 0 ?" It was answered by Pavlović with an example in which σ σ 0 [18]. The following diagram was obtained in [1].…”

“…Theorem 2.5. ( [18]) In any J-space (U, τ), each of the following conditions implies that M * = Γ(M) for any subset M of U: The family of all semi-open sets in a topological space (U, τ) is denoted by SO(U). Every open set is semi-open i.e.…”

“…Let U = ω + 1 = ω ∪ {ω} and the topology on it be the order topology. This topology can be expressed [18] as: τ = P(ω) ∪ {{ω} ∪ (ω \ K) : K ⊆ ω and K is finite}.…”

“…Two new topologies was obtained with this operator Ψ Γ . In [18], Pavlović gave an example that one of these two topologies is strictly finer than the other. The concept of weak semi-local function was defined and its basic properties were investigated in [24].…”

Common properties and approximations of local function and set operator $\psi$

“…Finally we have considered the expansion of above two operators. However A. Pavlovic [25] have studied "local function versus local closure function in ideal topological spaces".…”