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Transactions of the American Mathematical Society

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Triangulations of subanalytic sets and locally subanalytic manifolds

Authors: M. Shiota and M. Yokoi
Journal: Trans. Amer. Math. Soc. 286 (1984), 727-750
MSC: Primary 32B20; Secondary 57Q15
MathSciNet review: 760983
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Abstract: If two polyhedrons are locally subanalytically homeomorphic (that is, the graph is locally subanalytic), they are $ {\text{PL}}$ homeomorphic. A locally subanalytic manifold is one whose coordinate transformations are locally subanalytic. It is proved that a locally subanalytic manifold has a unique $ {\text{PL}}$ manifold structure. A semialgebraic manifold also is considered.

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Keywords: Triangulation, subanalytic, polyhedron, $ {\text{PL}}$ homeomorphism
Article copyright: © Copyright 1984 American Mathematical Society