• Kyungpook Mathematical Journal
• /
• v.27 no.1
• /
• pp.27-33
• /
• 1987

Minimal s-Urysohn and minimal s-regular spaces are studied. An s-Urysohn (respectively, s-regular) space (X, $\mathfrak{T}$) is said to be minimal s-Urysohn (respectively, minimal s-regular) if for no topology $\mathfrak{T}^{\prime}$ on X which is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) is s-Urysohn (respectively s-regular). Several characterizations and other related properties of these classes of spaces have been obtained. The present paper is a study of minimal P-spaces where P refers to the property of being an s-Urysohn space or an s-regular space. A P-space (X, $\mathfrak{T}$) is said to be minimal P if for no topology $\mathfrak{T}^{\prime}$ on X such that $\mathfrak{T}^{\prime}$ is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) has the property P. A space X is said to be s-Urysohn [2] if for any two distinct points x and y of X there exist semi-open set U and V containing x and y respectively such that $clU{\bigcap}clV={\phi}$, where clU denotes the closure of U. A space X is said to be s-regular [6] if for any point x and a closed set F not containing x there exist disjoint semi-open sets U and V such that $x{\in}U$ and $F{\subseteq}V$. Throughout the paper the spaces are assumed to be Hausdorff.

• Journal of applied mathematics & informatics
• /
• v.36 no.1_2
• /
• pp.59-68
• /
• 2018

In this paper, We define and explore the characterizations and properties of soft regular open(closed) and soft semi-regular sets in soft topological spaces. The properties of soft extremally disconnected spaces are also introduced and discussed. The findings in this paper will help researcher to enhance and promote further study on soft topology to carry out a general framework for their applications in practical life.

• Korean Journal of Mathematics
• /
• v.28 no.3
• /
• pp.573-585
• /
• 2020

We introduced the concepts of the generalized accumulation points and the generalized density of a subset of the Euclidean space in [1] and [2]. Using those concepts, we introduce the concepts of the generalized closure, the generalized interior, the generalized exterior and the generalized boundary of a subset and investigate some properties of these sets. The generalized boundary of a subset is closely related to the classical boundary. Finally, we also introduce and study a concept of the thickness of a subset.

• Communications of the Korean Mathematical Society
• /
• v.29 no.4
• /
• pp.555-568
• /
• 2014

A set with an operation defined on a family of subsets is studied. The operation is used to generalize the topological space itself. The operation defines the operation-open subsets in the set. Relations are studied among two types of the interiors and the closures of subsets. Some properties of maximal operation-open sets are obtained. Semi-open sets and pre-open sets are defined in the sets with operations and some relations among them are proved.

• Tunnel and Underground Space
• /
• v.2 no.2
• /
• pp.237-250
• /
• 1992

The cavities formed by the excavation of coal seam cause unstable within rock body, leading to large displacement around adjacent roadway. This displacement brings the closure of roadway and deformation of support. Therefore, it is necessary to understand and predict the deformation characteristics of roadway while coal seam is under excavation. In this study, the observed displacements are compared with the calculated ones through the analysis using Linear Boundary Element Mothod under the elastostatic conditions, in order to determine the virgin stress state and deformation modulus which affect the deformation characteristices.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.4
• /
• pp.671-677
• /
• 2006

Let $A, B{\in}B(H)$ be Hilbert space contractions, and let ${\Delta}_{AB}$ be the elementary operator ${\Delta}_{AB}:X{\rightarrow}AXB-X$. A number of conditions which are equivalent to '${\Delta}_{AB}$ has closed range' are proved.

• The Journal of the Korean dental association
• /
• v.24 no.7 s.206
• /
• pp.593-603
• /
• 1986

Segmented Arch technique은 edgewise mechanics의 한 줄기로서, 미국 코네티컬 주립대학 교정과 과장인 Dr. Burstone에 의하여서 1950년대 이래로 꾸준히 개발되어온 생역학적인 개념(biomechanical concept)을 가장 효율적으로 치료에 적용하고자 함에 있다고 하겠다. 저자는 Segmented arch technique의 최근의 경향과 치료이론 및 술식을 다음의 순서로 4회에 걸쳐서 소개하고자 한다. 1. 전치의 Intrusion에 의한 과개교합의 치료법 -Deep Overbite Correction 2. Space closure - 수평방향의 치아이동방법 3. Root movement의 방법 - Torque mechanics 4. 구치를 Upright 시키는 방법 - Tip back mechanics.

• The Pure and Applied Mathematics
• /
• v.14 no.1 s.35
• /
• pp.15-21
• /
• 2007

We introduce the notion of pre-convergence of p-stacks and characterize the pre-interior, pre-closure, separation axioms and pre-continuity on a topological space by using pre-convergence of p-stacks. We also introduce the notion of p-precompactness and investigate its properties in terms of pre-convergence of p-stacks.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1995.10b
• /
• pp.369-373
• /
• 1995

We introduce the concepts of generalized closed fuzzy set(breifly g-closed fuzzy set) and generalized fuzzy continuity (briefly g-fuzzy continuity), and investigate their some properties. When A is a fuzzy set in a fuzzy topological space, we denote the closure of A, the interior of A and the complement of A as CA(a) and CA, respectively

• The Journal of the Korean dental association
• /
• v.24 no.8 s.207
• /
• pp.698-702
• /
• 1986

Segmented Arch technique 은 edgewise mechanics의 한 줄기로서, 미국 코네티컬 주립대학 교정과 과장인 Dr. Burstone에 의하여 1950년대 이래로 꾸준히 개발되어온 치료술식으로서 그 특징을 한마디로 요약하면 생역학적인 개념(biomechanical concept)을 가장 효율적으로 치료에 적용하고자 함에 있다고 하겠다. 저자는 Segmented arch technique의 최근의 경향과 치료이론 및 술식을 다음의 순서로 4회에 걸쳐서 소개하고자 한다. 1. 전치의 Intrusion에 의한 과개교합의 치료법 -Deep Overbite Correction 2. Space closure - 수평방향의 치아이동방법 3. 치근의 이동방법 - Root movement 4. 구치를 Upright 시키는 방법 - Tip back mechanics