Algorithmic Counting of Zero-Dimensional Finite Topological Spaces With Respect to the Covering Dimension

作者：

Highlights：

• We specify the number of zero-dimensional topological spaces with respect to the covering dimension on the set 1,...,n.

• Based on this, we give algorithms for computing this number.

• A parallel implementation of a backtracking-algorithm in C using the libraries GMP and OpenMP allows to compute the number up to n = 19.

摘要

•We specify the number of zero-dimensional topological spaces with respect to the covering dimension on the set 1,...,n.•Based on this, we give algorithms for computing this number.•A parallel implementation of a backtracking-algorithm in C using the libraries GMP and OpenMP allows to compute the number up to n = 19.

论文关键词：Finite topological space,Covering dimension,Specialisation pre-order,Partial order,Set partition,Backtracking algorithm,Parallelisation,GMP,OpenMP,

论文评审过程：Received 21 April 2020, Revised 22 June 2020, Accepted 5 July 2020, Available online 25 August 2020, Version of Record 25 August 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125523