Computational approximations of compact metric spaces

Abstract

Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of $X$ that is a strong deformation retract. We provide a method to approximate the homology groups of $X$ and other algebraic invariants. Finally, we study computational aspects and the implementation of this method.

References in corpus (1)

• Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces

Cited by in corpus (1)

• Shape of compacta as extension of weak homotopy of finite spaces