• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.539-547
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• 2005

The class of b-open sets in the sense of $Andrijevi{\acute{c}}$ ([3]), was discussed by El-Atik ([9]) under the name of ${\gamma}-open$ sets. This class is closed under arbitrary union. The aim of this paper is to use ${\Lambda}-sets$ and ${\vee}-sets$ due to Maki ([15]) some topologies are constructed with the concept of b-open sets. $b-{\Lambda}-sets,\;b-{\vee}-sets$ are the basic concepts introduced and investigated. Moreover, several types of near continuous function based on $b-{\Lambda}-sets,\;b-{\vee}-sets$ are constructed and studied.

• Kyungpook Mathematical Journal
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• 제51권4호
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• pp.429-433
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• 2011

In this article we introduce the notion of b-locally open sets, $bLO^*$ sets, $bLO^{**}$ sets in bitopological spaces and obtain several characterizations and some properties of these sets.

• The Pure and Applied Mathematics
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• 제17권3호
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• pp.199-203
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• 2010

We introduce the notions of sg-semiopen set and other kinds of generalized sg-open sets and we investigate some properties for such generalized sg-open sets.

• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1259-1265
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• 2016

In this paper, we introduce the notions of mean open and closed sets in topological spaces, and obtain some properties of such sets. We observe that proper paraopen and paraclosed sets are identical to mean open and closed sets respectively.

• The Pure and Applied Mathematics
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• 제28권3호
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• pp.199-215
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• 2021

The purpose of this paper is to define and study some new classes of sets by using nano operation namely, ζ-nano regular open, ζ-nano open, ζ-nano α-open, ζ-nano pre-open, ζ-nano semi-open, ζ-nano b-open and ζ-nano β-open in nano topology. Some properties and the relationships between these sets and the related concepts are investigated. Also, we found the deciding factors for the most common disease fever.

• Korean Journal of Mathematics
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• 제25권3호
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• pp.437-453
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• 2017

A new class of sets, called generalized (${\Lambda}$, b)-closed sets, has been introduced and studied. Also, several properties of generalized (${\Lambda}$, b)-closed sets are investigated. Some characterizations of ${\Lambda}_b$-regular spaces and ${\Lambda}_b$-normal spaces are discussed.

• Journal of the Korean Statistical Society
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• 제25권2호
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• pp.243-253
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• 1996

Let X and Y be random vectors in R$^{n}$ . A random vector X is 'more associated' than Y if and only if P(X $\in$ A ∩ B) - P(X $\in$ A)P(X $\in$ B) $\geq$ P(Y $\in$ A ∩ B)-P(Y $\in$ A)P(Y $\in$ B) for all open upper sets A and B. By requiring the above inequality to hold for some open upper sets A and B various notions of positive dependence orderings which are weaker than 'more associated' ordering are obtained. First a general theory is given and then the results are specialized to some concepts of a particular interest. Various properties and interrelationships are derived.

• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.223-238
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• 1994

A random vector $\b{X} = (X_1,\cdots,X_n)$ is weakly associated if and only if for every pair of partitions $\b{X}_1 = (X_{\pi(1)},\cdots,X_{\pi(k)}), \b{X}_2 = (X_{\pi(k+1),\cdots,X_{\pi(n)})$ of $\b{X}, P(\b{X}_1 \in A, \b{X}_2 \in B) \geq P(\b{X}_1 \in A)\b{P}(\b{X}_2 \in B)$ whenever A and B are open upper sets and $\pi$ is a permutation of ${1,\cdots,n}$. In this paper, we develop notions of weak positive dependence, which are weaker than a positive version of negative association (weak association) but stronger than positive orthant dependence by arguments similar to those of Shaked. We also illustrate some concepts of a particular interest. Various properties and interrelationships are derived.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.341-348
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• 2013

In this paper, the concept of supra $b$-irresolute maps is introduced and several properties of it is investigated. Furthermore, the notion of supra $b$-connectedness is defined and researched by means of supra $b$-separated sets.

• Journal of the Korean Mathematical Society
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• 제36권4호
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• pp.649-662
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• 1999

A random vector =(X1,…, Xn) is conditionally weakly associated if and only if for every pair of partitions 1=(X$\pi$(k+1),…,X$\pi$(k)), 2=(X$\pi$(k+1),…,X$\pi$(n)) of P(1$\in$A│2$\in$B, $\theta$$\in$I) $\geq$P$\in$A│$\theta$$\in$I whenever A and B are open upper sets and $\pi$ is any permutation of {1,…,n}. In this note we develop some concepts of conditional positive dependence, which are weaker than conditional weak association but stronger than conditional positive orthant dependence, by requiring the above inequality to hold only for some upper sets and applying the arguments in Shaked (1982).