• 대한수학회논문집
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• 제26권2호
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• pp.297-304
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• 2011

In this paper, we introduce closure operators [${\cdot}$]c and [${\cdot}$]a on a space and study some relations among [${\cdot}$]c, [${\cdot}$]a and countable tightness. We introduce the concepts of a strongly sequentially closed set and a strongly sequentially open set and show that a space X has countable tightness if and only if every strongly sequentially closed set is closed if and only if every strongly sequentially open set is open. Finally we find a generalization of the weak Fr$\'{e}$chet-Urysohn property which is equivalent to countable tightness.

• 대한수학회논문집
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• 제28권2호
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• pp.335-351
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• 2013

In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W-mappings of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings.

• 대한수학회보
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• 제52권5호
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• pp.1737-1751
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• 2015

For every doubling gauge g, we prove that there is a Cantor set of positive finite $H^g$-measure, $P^g$-measure, and $P^g_0$-premeasure. Also, we show that every compact metric space of infinite $P^g_0$-premeasure has a compact countable subset of infinite $P^g_0$-premeasure. In addition, we obtain a class of uniform Cantor sets and prove that, for every set E in this class, there exists a countable set F, with $\bar{F}=E{\cup}F$, and a doubling gauge g such that $E{\cup}F$ has different positive finite $P^g$-measure and $P^g_0$-premeasure.

• Kyungpook Mathematical Journal
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• 제28권1호
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• pp.91-95
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• 1988

The nature of a H-set in a Hausdorff space is not well understood. In this note it is shown that if X is a countable union of nowhere dense compact sets, then X is not H-embeddable in any Hausdorff space. An example is given to show that there exists a non-Urysohn, non-H-closed space X such that each H-set of X is compact.

• 호남수학학술지
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• 제38권3호
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• pp.643-659
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• 2016

In this paper, we investigate some new results in MV-algebras and (strong) hyper MV-algebras. We show that for any infinite countable set M, we can construct an MV-algebra and a strong hyper MV-algebra on M. Specially, for any infinite totally bounded set, we can construct a strong hyper MV-algebra on it. Then by considering the concept of fundamental relation on hyper MV-algebras, we define the notion of fundamental MV-algebra and prove that any MV-algebra is a fundamental MV-algebra. In practical, we show that any infinite countable MV-algebra is a fundamental MV-algebra of itself, but it is not correct for finite MV-algebras.

• East Asian mathematical journal
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• 제39권5호
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• pp.515-522
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• 2023

In the case that the set of sorts is countable, we will prove that any sorted profinite group has the unique SEP-cover using the notion of prime model in model theory.

• 대한수학회논문집
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• 제21권3호
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• pp.429-432
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• 2006

We use Cauchy's functional equation to construct a new non-measurable set which is a (vector) subspace of \mathbb{R}$ and is of a codimensiion 1, considering \mathbb{R}$, the set of real numbers, as a vector space over a field \mathbb{Q}$ of rational numbers. Moreover, we show that \mathbb{R}$ can be partitioned into a countable family of disjoint non-measurable subsets.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권2호
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• pp.149-156
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• 1995

In stability theory of polysystems two concepts that playa very important role are the limit set and the prolongational limit set. For the above two concepts, A.Bacciotti and N.Kalouptsidis studied their properties in a locally compact metric space [2]. In this paper we investigate their results in c-first countable space which is more a general space than a metric space.(omitted)

• 한국수학사학회지
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• 제22권4호
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• pp.115-128
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• 2009

본 논문에서 von Neumann의 공리계를 수정하여 새로운 DVN공리계를 소개한다. 그리고 DVN공리계에서 불가지 류의 존재성을 조사하고, 불가지류와 선택공리의 관계를 논한다.

• 대한수학회논문집
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• 제26권2호
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• pp.215-227
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• 2011

In this paper we introduce a class $h^{-\infty}_{\Phi}(\mathbb{B})$ of weighted spaces of harmonic functions in the unit ball $\mathbb{B}$ of $\mathbb{R}^n$. We dene weakly sufficient sets in this space and give an explicit construction of countable sets of such a type. Various examples of weight functions are also discussed.