• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.553-563
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• 2017

Different topological dimensions related to the pseudo-prime spectrum of topological modules are studied. An example of topological modules is introduced. Also, we give a result about Noetherianness of the pseudo-prime spectrum of topological modules.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.23-76
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• 1998

We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.

• The Pure and Applied Mathematics
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• v.14 no.1 s.35
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• pp.1-5
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• 2007

We study the topological magnitude of a special subset from the distribution subsets in a self-similar Cantor set. The special subset whose every element has no accumulation point of a frequency sequence as some number related to the similarity dimension of the self-similar Cantor set is of the first category in the self-similar Cantor set.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.153-161
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• 2016

It is shown that the algebra $\mathfrak{H}^{\infty}$ of bounded Dirichlet series is not a coherent ring, and has infinite Bass stable rank. As corollaries of the latter result, it is derived that $\mathfrak{H}^{\infty}$ has infinite topological stable rank and infinite Krull dimension.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.128-132
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• 2002

One of the fundamental components important to the analysis of spatial objects is to represent topological relationships between spatial features. Users of geographic information systems retrieve a lot of objects from spatial database and analyze their condition by means of topological relationships. The existing methods that represent these relationships have the disadvantage that they have limited information in $R^2$. In this paper, we represent and define the topological relationships between 3-dimensional spatial objects using the several representing methods of 2-dimensional features. We use the diverse representing methods, which include the 4-, 9-intersection, dimension extended and calculus-based method. Furthermore, we discuss OGC's topological relationships and operators for 3-dimensional spatial data.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.612-614
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• 2003

In this paper we propose four-dimensional (4D) operators, which can be used to deal with sequential changes of topological relationships between 4D moving objects and we call them 4D development operators. In contrast to the existing operators, we can apply the operators to real applications on 4D moving objects. We also propose a new approach to define them. The approach is based on a dimension-separated method, which considers x-y coordinates and z coordinates separately. In order to show the applicability of our operators we show the algorithms for the proposed operators and development graph between 4D moving objects.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1285-1307
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• 2019

For a multiplication R-module M we consider the Zariski topology in the set Spec (M) of prime submodules of M. We investigate the relationship between the algebraic properties of the submodules of M and the topological properties of some subspaces of Spec (M). We also consider some topological aspects of certain frames. We prove that if R is a commutative ring and M is a multiplication R-module, then the lattice Semp (M/N) of semiprime submodules of M/N is a spatial frame for every submodule N of M. When M is a quasi projective module, we obtain that the interval ${\uparrow}(N)^{Semp}(M)=\{P{\in}Semp(M){\mid}N{\subseteq}P\}$ and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.261-275
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• 2011

We give characterizations of the differentiability points and the non-differentiability points of the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) singulr function using the distribution sets in the unit interval. Using characterizations, we show that the Hausdorff dimension of the non-differentiability points of the RNT singular function is greater than 0 and the packing dimension of the infinite derivative points of the RNT singular function is less than 1. Further the RNT singular function is nowhere differentiable in the sense of topological magnitude, which leads to that the packing dimension of the non-differentiability points of the RNT singular function is 1. Finally we show that our characterizations generalize a recent result from the ($\tau$, $\tau$ - 1)-expansion associated with the RNT singular function adding a new result for a sufficient condition for the non-differentiability points.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.8
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• pp.60-71
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• 1996

Mostof existing CAD systems do not provide the advanced function for systematic checking of design and drafting errors in mechanical drawings. We have reported a computer aided drawing check system to single plane projection drawings made by a CAD system. This paper describes a checking method of dimensioning errors in mechanical drawings. The checking items are deficiency and redundancy of dimensions, input-errors in dimension figures and symbols, etc. Checking for deficiency and redundancy of global dimensions has been performed applying Graph Theory. This system has been applied to several examples and we have confirmed the feasibility of this checking method.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.563-575
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• 2003

We show that if a connected Stein manifold M of dimension n has the holomorphic automorphism group Aut(M) isomorphic to $Aut(C^k {\times}(C^*)^{n - k})$ as topological groups, then M itself is biholomorphically equivalent to C^k{\times}(C^*)^{n - k}$. Besides, a new approach to the study of U(n)-actions on complex manifolds of dimension n is given.