紧族对可定义集的逼近及同伦和同调的上界
Approximation of definable sets by compact families, and upper bounds on homotopy and homology
摘要：
证明了o-极小集的同伦群和同调群在紧o-极小集逼近下的新的上界。特别地，我们改进了由无量词公式定义的半代数集的贝蒂数的已知上界，并首次得到了子Pfiran集的贝蒂数的一个单指数界.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
