A note on mathematical structures

Modak, Shyamapada; Noiri, Takashi

doi:10.5269/bspm.v37i1.32085

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B Soc Paran Mat

2017

DOI: 10.5269/bspm.v37i1.32085

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A note on mathematical structures

Shyamapada Modak

Takashi Noiri

Abstract: In this paper we shall discuss the interrelations between generalizations of topology and mathematical structures. We also discuss the algebraic nature of generalizations of topology and mathematical structures.

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2020

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References 11 publications

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

Abu-Donia

Hosny

2020

J Egypt Math Soc

View full text Add to dashboard Cite

show abstract

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A note on mathematical structures

Abstract: In this paper we shall discuss the interrelations between generalizations of topology and mathematical structures. We also discuss the algebraic nature of generalizations of topology and mathematical structures.

Cited by 1 publication

References 11 publications

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

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

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