• Honam Mathematical Journal
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• v.41 no.4
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• pp.851-861
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• 2019

In this paper we consider proper semialgebraic actions of semialgebraic groups on semialgebraic sets. We prove the equivariant version of the semialgebraic local-triviality of semialgebraic maps.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.4
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• pp.245-253
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• 2023

Let G be a semialgebraic group not necessarily compact. In this paper, we prove that the orbit space of every proper semialgebraic G-set has a semialgebraic structure.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.371-386
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• 1998

Let G be a compact Lie group and M a semialgebraic G space in some orthogonal representation space of G. We prove that if G is finite then M has an equivariant semialgebraic triangulation. Moreover this triangulation is unique. When G is not finite we show that M has a semialgebraic G CW complex structure, and this structure is unique. As a consequence compact semialgebraic G space has an equivariant simple homotopy type.

• Honam Mathematical Journal
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• v.34 no.4
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• pp.495-504
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• 2012

Let G be a semialgebraic group and M a proper semi-algebraic G-set which is locally complete. In this paper we show that the orbit space M/G has a semialgebraic structure such that the orbit map is semialgebraic.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.13-23
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• 2022

Let G be a semialgebraic group not necessarily compact. Let M be a proper semialgebraic G-set whose orbit space has a semialgebraic structure. In this paper, we prove the embeddability of M into a G-representation space when G is linear.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.179-188
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• 2007

We prove the equivariant version of the semialgebraic local-triviality of semialgebraic maps.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.629-646
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• 2004

Let G be a compact semialgebraic group and M a semi-algebraic G-set. We prove that there exists a semialgebraic slice at every point of M. Moreover M can be covered by finitely many semialgebraic G-tubes. As an application we give a different proof that every semialgebraic G-set admits a semi algebraic G-embedding into some semialgebraic orthogonal representation space of G, which has been proved in [15].

• Honam Mathematical Journal
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• v.37 no.4
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• pp.431-440
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• 2015

Let G be a semialgebraic group which is not necessarily compact. Let X be a semialgebraically proper G-set such that the orbit space has a semialgebraic structure. In this paper we prove the existence of semialgebraic slices of X. Moreover X can be covered by finitely many semialgebraic G-tubes.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.101-113
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• 2017

Let G be a semialgebraic group which is not necessarily compact. Let X be a proper semialgebraic G-set whose orbit space has a semialgebraic structure. In this paper we prove that X has a finite open straight G-CW complex structure.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.319-327
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• 2013

In this paper we compare the notion of proper map in the category of topological spaces with that in the category of semialgebraic sets. To do this, we find some equivalence conditions for semialgebraically proper maps. In particular, we prove that a continuous semialgebraic map is semialgebraically proper if and only if it is proper. Moreover, we compare the semialgebraically proper map with the proper map in the sense of Delfs and Knebush [4].