标题： 有限空间的一点约简，h-正则CW复形和可缩性 显示英文标题

标题： One-point reductions of finite spaces, h-regular CW-complexes and collapsibility

摘要： 我们研究有限拓扑空间的一点约简方法。 这些方法允许通过其有限模型的初等移动来研究细胞复形的同伦理论。 我们还引入了h-正则CW复形的概念，该概念推广了正则CW复形的概念，并证明了h-正则CW复形，作为一种至多同伦意义下的组合对象，可以通过其相关的有限空间进行建模（在同伦意义下）。 这是通过推广McCord关于单纯复形的经典结果来实现的。 显示英文摘要

摘要： We investigate one-point reduction methods of finite topological spaces. These methods allow one to study homotopy theory of cell complexes by means of elementary moves of their finite models. We also introduce the notion of h-regular CW-complex, generalizing the concept of regular CW-complex, and prove that the h-regular CW-complexes, which are a sort of combinatorial-up-to-homotopy objects, are modeled (up to homotopy) by their associated finite spaces. This is accomplished by generalizing a classical result of McCord on simplicial complexes.