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arXiv · 1612.04187

How to find finite topological spaces with given quotient-spaces

J. M. S. Simoes-Pereira
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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.

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J. M. S. Simoes-Pereira. 2018-06-21. How to find finite topological spaces with given quotient-spaces. https://arxiv.org/abs/1612.04187

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