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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Approximating embeddings of polyhedra in codimension three

Author: J. L. Bryant
Journal: Trans. Amer. Math. Soc. 170 (1972), 85-95
MSC: Primary 57C35; Secondary 57C55
MathSciNet review: 0307245
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Abstract: Let $ P$ be a $ p$-dimensional polyhedron and let $ Q$ be a PL $ q$-manifold without boundary. (Neither is necessarily compact.) The purpose of this paper is to prove that, if $ q - p \geqslant 3$, then any topological embedding of $ P$ into $ Q$ can be pointwise approximated by PL embeddings. The proof of this theorem uses the analogous result for embeddings of one PL manifold into another obtained by Černavskiĭ and Miller.

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Keywords: PL embedding, PL mapping, PL approximation, polyhedron, PL manifold
Article copyright: © Copyright 1972 American Mathematical Society