• Honam Mathematical Journal
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• v.24 no.1
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• pp.87-91
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• 2002

This note consists of some efficient examples to support the notion of enveloping semigroup compactification and also employ this notion to obtain the universal reductive compactification.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.745-763
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• 2017

The Borel-Serre partial compactification gives cofinite models for the proper classifying space for arithmetic lattices. Non-arithmetic lattices arise only in semisimple Lie groups of ${\mathbb{R}}$-rank one. The author generalizes the Borel-Serre partial compactification to construct cofinite models for the proper classifying space for lattices in semisimple Lie groups of ${\mathbb{R}}$-rank one by using the reduction theory of Garland and Raghunathan.

• The Pure and Applied Mathematics
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• v.23 no.4
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• pp.329-337
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• 2016

In this paper, we show that every compactification, which is a quasi-F space, of a space X is a Wallman compactification and that for any compactification K of the space X, the minimal quasi-F cover QFK of K is also a Wallman compactification of the inverse image ${\Phi}_K^{-1}(X)$ of the space X under the covering map ${\Phi}_K:QFK{\rightarrow}K$. Using these, we show that for any space X, ${\beta}QFX=QF{\beta}{\upsilon}X$ and that a realcompact space X is a projective object in the category $Rcomp_{\sharp}$ of all realcompact spaces and their $z^{\sharp}$-irreducible maps if and only if X is a quasi-F space.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1037-1048
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• 1997

We show that an asymptotically Euclidean scalar-flat Kahler metric ona complex surface can be smoothly conformally compactified at the infinity point. We discuss some implication of this, characterizing such metrics on $C^2$ blown up at some points.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.445-464
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• 2013

We describe the one-dimensional and zero-dimensional cusps of the Satake compactification for the paramodular groups in degree two for arbitrary levels. We determine the crossings of the one-dimensional cusps. Applications to computing the dimensions of Siegel modular forms are given.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.81-86
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• 2005

In this paper, we consider locally compact Hausdorff spaces having the closed unit interval of the real line as the remainder for an ESH-compactification and obtain that in the class of compact maps the extensions of homotopic maps on the respective ESH-compactifications remain homotopic under certain conditions.

• Journal of Industrial Technology
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• v.6
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• pp.9-12
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• 1986

이 논문(論文)에서는 net와 연속함수(連續函數)의 족(族)에서 상(像)에 의한 Compact 공간(空間)의 성질(性質)을 조사하였다. Compact 공간(空間)에 기초를 둔 C-closed, A-net, A-변환(變換)을 사용하여 Haussdorff 공간(空間) 혹은 Regular 공간(空間)에서의 그들의 성질(性質)을 살펴보았다.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.525-527
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• 2019

Let X be a completely regular space and let β(X) be the Stone-Čech compactification of X. A flow 𝜙 on X can be extended to a flow 𝚽 on β(X).

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.609-616
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• 2011

Observing that $vX{\times}vY$ is a Wallman realcompactification of $X{\times}Y$ if $v(X{\times}vY)=vX{\times}vY$, we show that $v(X{\times}Y)=vX{\times}vY$ if and only if $X{\times}Y$ is z-embedded in $vX{\times}vY$ and $vX{\times}vY$ is a Wallman compactification of $X{\times}Y$.

• Bulletin of the Korean Mathematical Society
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• v.13 no.1
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• pp.7-13
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• 1976