• 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.

• 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.

• 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].