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Preprint Number 2538
2538. Saugata Basu and Alison Rosenblum Equivariance in Approximation by Compact Sets E-mail: Submission date: 27 December 2023 Abstract:
We adapt a construction of Gabrielov and Vorobjov for use in the symmetric
case. Gabrielov and Vorobjov had developed a means by which one may replace an
arbitrary set S definable in some o-minimal expansion of ℝ with a
compact set T. T is constructed in such a way that for a given m>0 we
have epimorphisms from the first m homotopy and homology groups of T to
those of S. If S is defined by a boolean combination of statements h(x)=0
and h(x)>0 for various h in some finite collection of definable continuous
functions, one may choose T so that these maps are isomorphisms for 0 ≤
k ≤ m-1. In this case, T is also defined by functions closely related to
those defining S. Mathematics Subject Classification: 14P99 (Primary) 03C64 (Secondary) Keywords and phrases: |
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