Properties of S-closed spaces

Noiri, Takashi

doi:10.1007/bf01886314

Cited by 22 publications

(27 citation statements)

References 9 publications

(11 reference statements)

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“…DEFINITION 2.4. A subset A of a topological space (X, R) is said to be semiregular [8] if it is semi-open and semi-closed. The family of all semi-regular sets of (X,T) is denoted by SR(X).…”

Section: If For Each X € a There Exists A Regular Open Set G Of X Sucmentioning

confidence: 99%

SOME PROPERTIES OF UPPER AND LOWER Θ-Quasicontinuous MULTIFUNCTIONS

Noiri¹,

Popa

2005

Demonstratio Mathematica

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Abstract. In this paper we obtain new characterizations of upper and lower 0-quasicontinuous multifunctions and investigate several properties of such multifunctions. IntroductionIn 1963, Levine [14] introduced the notion of semi-continuity in topological spaces. Arya and Bhamini [4] introduced the notion of 0-semi-continuity as a generalization of semi-continuity. Recently, Noiri [19] and Jafari and Noiri [12] have further investigated properties of 0-semi-continuity. The present authors [23] introduced and studied 0-quasicontinuous multifunctions.In this paper we shall obtain new characterizations of upper /lower 0-quasicontinuous multifunctions and investigate several further properties of such multifunctions. PreliminariesThroughout the present paper, (X, r) and (Y, cr) (or simply X and Y) always represent topological spaces. Let A be a subset of X. The closure of A and the interior of A are denoted by C1(A) and Int(A), respectively. A subset A is said to be regular closed (resp. regular open) if Cl(Int(j4)) = A (resp. Int(Cl(>l)) = A). The 6-closure of A, denoted by Cle(-A), is defined to be a set of all x 6 X such that C1 (

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Section: If For Each X € a There Exists A Regular Open Set G Of X Sucmentioning

confidence: 99%

SOME PROPERTIES OF UPPER AND LOWER Θ-Quasicontinuous MULTIFUNCTIONS

Noiri¹,

Popa

2005

Demonstratio Mathematica

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“…The complement of a semi-open (resp., preopen, α-open, β-open) set is said to be semi-closed (resp., preclosed, α-closed, β-closed, or semi-preclosed). If A is both semi-open and semi-closed, then it is said to be semi-regular [9]. If A is both β-open and β-closed, then it is said to be semipre-regular or β-clopen.…”

Section: Preliminariesmentioning

confidence: 99%

Slightly β‐continuous functions

Noiri¹

2001

International Journal of Mathematics and Mathematical Sciences

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“…A set A is called semi-regular [5] if it is both semi-open and semi-closed. Di Maio and Noiri [5] have shown that a set A is semi-regular if and only if there exists a regular open set U with U ⊆ A ⊆ cl(U ).…”

Section: P-closed Subspaces Recall That a Topological Space (X τ) Imentioning

confidence: 99%

“…Di Maio and Noiri [5] have shown that a set A is semi-regular if and only if there exists a regular open set U with U ⊆ A ⊆ cl(U ). Cameron [3] used the term regular semi-open for a semi-regular set.…”

Section: P-closed Subspaces Recall That a Topological Space (X τ) Imentioning

confidence: 99%