Some New Topologies on Ideal Topological Spaces

Modak, Shyamapada

doi:10.1007/s40010-012-0039-3

Cited by 13 publications

(9 citation statements)

References 11 publications

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“…[18] called such ideal as ' -boundary' whereas Dontchev [27] called such spaces as 'Hayashi-Samuel' spaces. In fact such ideals play a very important role in the study of ideals (see: [6,19,28,29,30]).…”

Section: Common Propertiesmentioning

confidence: 99%

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

Modak

Selim

Islam

2020

Cumhuriyet Science Journal

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Section: Common Propertiesmentioning

confidence: 99%

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

Modak

Selim

Islam

2020

Cumhuriyet Science Journal

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“…We can say that ψ * : (X, w, H) −→ C(X, w), (where C(X, w) is a class of all w-closed sets in (X, w)), is a set operator and it is defined as ψ * (S) = (ψ(S)) * for A ⊂ X . Although, Modak and Bandyopadhyay in [17], Modak in [18] and Modak and Islam in [13] have introduced similar types of set ψ H -semiopen, ψ * H -semiopen and the similar type of operator ψ * in the ideal topological space.…”

Section: Examplementioning

confidence: 99%

On $$\psi _{{\mathcal{H}}}( . )$$-operator in weak structure spaces with hereditary classes

Abu-Donia

Hosny

2020

J Egypt Math Soc

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Weak structure space (briefly, wss) has master looks, when the whole space is not open, and these classes of subsets are not closed under arbitrary unions and finite intersections, which classify it from typical topology. Our main target of this article is to introduce $$\psi _{{\mathcal {H}}}(.)$$ ψ H ( . ) -operator in hereditary class weak structure space (briefly, $${\mathcal {H}}wss$$ H w s s ) $$(X, w, {\mathcal {H}})$$ ( X , w , H ) and examine a number of its characteristics. Additionally, we clarify some relations that are credible in topological spaces but cannot be realized in generalized ones. As a generalization of w-open sets and w-semiopen sets, certain new kind of sets in a weak structure space via $$\psi _{{\mathcal {H}}}(.)$$ ψ H ( . ) -operator called $$\psi _{{\mathcal {H}}}$$ ψ H -semiopen sets are introduced. We prove that the family of $$\psi _{{\mathcal {H}}}$$ ψ H -semiopen sets composes a supra-topology on X. In view of hereditary class $${\mathcal {H}}_{0}$$ H 0 , $$w T_{1}$$ w T 1 -axiom is formulated and also some of their features are investigated.

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“…Let ( , , ) X  be an ideal topological space and AX  . Then, A is said to be a *  -set [9] (resp.  -C set [12], regular open set [27]…”

Section:  Is Calledmentioning

confidence: 99%