[PDF] Top 20 Some Remarks on Semi Open Sets with Respect to an Ideal

... Example 1. Let X = { a, b, c, d } with topology τ = { X , ; , { a, c } , { a, b, c }} and I = {;} . Notice that the collection of nonempty subsets of X satisfies the finite intersection property and every nonempty ... See full document

... define semi-open sets with respect to an ideal I , and also study some of their ...of semi-open sets with respect to a given ideal I ... See full document

... An ideal I on a topological space (X , τ) is a nonempty collection of subsets of X which satisfies (i) A ∈ I and B ⊂ A implies B ∈ I and (ii) A ∈ I and B ∈ I implies A ∪ B ∈ I ...an ideal I on X and if P (X ... See full document

... of semi-open sets in bitopological ...defined semi-preopen (β-open)sets in bitopological ...An ideal I on a topological space (X, τ ) is a collection of subsets of X ... See full document

... Proof: Let G be a W-R*-I closed set in (X,  , I).Suppose H is a regular semi closed set such that H  Cl*(int (G))\G. Since G is W-R*-I closed set, it follows from theorem 5.6 that H=  .Thus, we have H  ... See full document

... never open in and of itself. Rather, a set is open only with respect to a specific metric space containing ...not open when considered as a subset of the real line because any open ... See full document

... of ideal topological ...defining ideal topological space which has its application in localization theory in set topology by Vaidyanathaswamy ...I-open sets with respect to an ... See full document

... A = ∅. This implies that x 6∈ A s0 . But this is a contradiction. Hence, it must be that A s0 = ∅. We explain that the three properties mentioned in the above theorem need not be true if (X, µ) does not have the ... See full document

... application ideal topological spaces. Khan and Noiri [ 3 ] have introduced semi-local functions in ideal topological ...introduced some of properties of I g -closed sets and I g ... See full document

... an ideal on X. A subset A ⊂ X is said to be generalized open with respect to an ideal (briefly Ig-open) if and only if X–A is ...for some U ∈ I, whenever F ⊂ A and F is ... See full document

... Let ᏿(X,Y ) denote the set of strictly singular operators from X into Y . In general, strictly singular operators are not compact (see [12, 4]). If X = Y , ᏿(X) : = ᏿(X,X) is a closed two-sided ideal of ᏸ (X) ... See full document

... minimal open sets in topological ...minimal open set is ...minimal open sets, we obtain a sufficient condition for a locally finite space to be a pre- Hausdorff ... See full document

... In this section the notion of ij -t-open sets is introduced in bitopological spaces and their relationships with p-sets, q-sets, b-open sets, semi-open sets and pre-open sets are[r] ... See full document

... tri semi-open sets and fuzzy tri pre-open sets, fuzzy tri continuous function, fuzzy tri semi-continuous function and fuzzy tri pre-continuous functions and their basic ... See full document

... [5] Kandil A., Biproximities and fuzzy bitopological spaces, Simon Steven 63(1989) ,45-66. [6]Kovar, M.,(2000).On 3-Topological version of Thet-Reularity. Internat.J.Matj,Sci. ,23(6),393-398. [7] Levine N.(1963). ... See full document

... Also he introduced the notion of semi open sets in topological spaces .Bhattacharyya and Lahiri [1] introduced a class of sets called semi generalized closed sets by means of semi o[r] ... See full document

... © 2017, IJMA. All Rights Reserved 153 Example 6.8: Let X =Y={a, b, c}, τ = {ϕ ,{a},{b},{a, b},X} , σ = { ϕ , {a},{c},{a, b}, {a, c}, Y}, and σ c = { ϕ , {b},{c},{a, b}, {b, c}, Y}, then S* δO(X, τ) = {ϕ , {a},{b},{a, ... See full document

... Example 2.9. Let X = {a, b, c}, τ = {∅, X, {a}, {b}, {a, b}}. Then λ(X) = {∅ , X, { a } , { b } , { a, b } , { a, c } , { b, c }} and C(λ(X)) (all λ-closed sets in X) = {∅ , X, { b, c } , { a, c } , { c } , { b } ... See full document

... Definition 3.1: A function f :X⟶Y is said to be semi*αcontinuous at xX if for each open set V of Y containing fx, there is a semi*α-open set U in X such that xU and fU⊆V.. Then the fol[r] ... See full document

... investigated. Some results about existence of maximal m-open sets are ...m-open sets in an m-space and maximal open sets in the corresponding generated topology are ... See full document