In this paper, we extend the notions of γ-operation introduced in [12], by using the soft ideal notions. We introduce the notions of Ĩ-open soft sets, pre-Ĩopen soft sets, α-Ĩ-open soft sets, semi-Ĩ-open soft sets and β-Ĩ-open soft sets to soft topological spaces. We study the relations between these different types of subsets of soft topological spaces with soft ideal. We also introduce the co...

In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...

The notions of pre-local function, semi-local functions and α-local functions with respect to a topology and an ideal are introduced, and several properties are investigated. Also, the concept of P -I-open sets and P -I-closed sets in ideal topological spaces are discussed. Relations between I-open sets and P -I-open sets are provided, and several properties related to P -I-open sets, pre-local...

Several specific types of generalized sets (briefly, g-T_g-sets in topological spaces T_g-spaces have been defined and investigated for various purposes from time to the literature T_g-spaces. Our recent research field a new class is reported herein as starting point more classes. It shown that superclass those whose elements are called open, closed, semi-open, semi-closed, pre-open, pre-closed...

Today’s housing, as a private realm of human life, has changed in comparison with the past which was made regardless of quality, desirability, and lack of paying attention to the human needs and its psychological consequences; That is to say, residential units have turned into a set of closed spaces and their open and semi-open spaces have been merged into the urban spaces which disrupted their...

We have introduced and investigated the notion of I-extremal disconnectedness on ideal topological spaces. First, we found that the notions of extremal disconnectedness and I-extremal disconnectedness are independent of each other. About the letter one, we observed that every open subset of an I-extremally disconnected space is also an I-extremally disconnected space. And also, in extremally di...

Some corrections to the papers \Some Generalizations of TD-Spaces (Mat. Ves-nik 34 (1982), 221{230)" and \A Generalization of Normal Spaces (ibid. 35 (1983), 1{10)" are given. 1. Semi-T D spaces 1] The rst part of the proofs of Theorems 1.6 and 2.4 of 1] are incorrect. The following two Theorems and their proofs provide the statements and proofs of the rst parts of the Theorems 1.6 and 2.4 of 1...

The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex non-commutative basic open semi-algebraic set (defined below). The main theorem of this paper is a converse, a result which has implications for both semidefinite programming and systems engineering. A non-commutative basic open semi-algebraic set is defined in terms of a non-commutative `×`-matrix polynomial p(x1 · · ...

The concept of a preopen set in a topological space was introduced by H. H. Corson and E. Michael in 1964 [3]. A subset A of a topological space (X, τ) is called preopen or locally dense or nearly open if A ⊆ Int(Cl(A)). A set A is called preclosed if its complement is preopen or equivalently if Cl(Int(A)) ⊆ A. The term, preopen, was used for the first time by A. S. Mashhour, M. E. Abd El-Monse...