• 제목/요약/키워드: semialgebraic

검색결과 11건 처리시간 0.017초

SEMIALGEBRAIC G CW COMPLEX STRUCTURE OF SEMIALGEBRAIC G SPACES

  • Park, Dae-Heui;Suh, Dong-Youp
    • 대한수학회지
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    • 제35권2호
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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.

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THE EXISTENCE OF SEMIALGEBRAIC SLICES AND ITS APPLICATIONS

  • Choi, Myung-Jun;Park, Dae-Heui;Suh, Dong-Youp
    • 대한수학회지
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    • 제41권4호
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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].

THE EQUIVALENCE CONDITIONS FOR SEMIALGEBRAICALLY PROPER MAPS

  • Park, Dae Heui
    • 호남수학학술지
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    • 제35권2호
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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].