How to find finite topological spaces with given quotient-spaces
Abstract
Our main problem is to find finite topological spaces to within homeomorphism, given (also to within homeomorphism) the quotient-spaces obtained by identifying one point of the space with each one of the other points. In a previous version of this paper, our aim was to reconstruct a topological space from its quotient-spaces; but a reconstruction is not always possible either in the sense that several non-homeomorphic topological spaces yield the same quotient-spaces, or in the sense that no topological space yields an arbitrarily given family of quotient-spaces. In this version of the paper we present an algorithm that detects, and deals with, all these situations.
Keywords
Cite
@article{arxiv.1612.04187,
title = {How to find finite topological spaces with given quotient-spaces},
author = {J. M. S. Simoes-Pereira},
journal= {arXiv preprint arXiv:1612.04187},
year = {2018}
}
Comments
This 22-pages paper is hard work, the algorithm is long and not easy to verify. Comments are welcome