Approximation of definable sets by compact families, and upper bounds on homotopy and homology
Approximation of definable sets by compact families, and upper bounds on homotopy and homology
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可定义集合的紧族逼近以及同伦和同调的上限
DOI：
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发表时间：
2007
期刊：
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通讯作者：
Nicolai N. Vorobjov
中科院分区：
文献类型：
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作者：
A. Gabrielov;Nicolai N. Vorobjov
我们根据紧致 o 极小集的近似证明了 o 极小集的同伦和同源群的新上限。特别是，我们改进了由无量词公式定义的半代数集贝蒂数的已知上限，并首次获得了亚普法夫集贝蒂数的单指数界。
We prove new upper bounds on homotopy and homology groups of o‐minimal sets in terms of their approximations by compact o‐minimal sets. In particular, we improve the known upper bounds on Betti numbers of semialgebraic sets defined by quantifier‐free formulae and obtain, for the first time, a singly exponential bound on Betti numbers of sub‐Pfaffian sets.