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Abstract: Arguments on PL,=piecewise linear topology work over any ordered field inthe same way as over the real field, and those on differential topology do overa real closed field R in an o-minimal structure that expands R,<,0,1,+,cdot.One of the most fundamental properties of definable sets is that a compactdefinable set in R^n is definably homeomorphic to a polyhedron see v. Weshow uniqueness of the polyhedron up to PL homeomorphisms o-minimalHauptvermutung. Hence a compact definable topological manifold admits uniquelya PL manifold structure and is, so to say, tame. We also see that many problemson PL and differential topology over R can be translated to those over the realfield.



Author: Masahiro Shiota

Source: https://arxiv.org/







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