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arXiv · 1910.12228

Ring-theoretic approaches to point-set topology

Abolfazl Tarizadeh
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Abstract

In this paper, it is shown that a topological space $X$ is compact iff every maximal ideal of the power set ring $\mathcal{P}(X)$ converges to exactly one point of $X$. Then as an application, simple and ring-theoretic proofs are provided for the Tychonoff theorem and Alexander subbase theorem. As another result in this spirit, a ring-theoretic proof is given to the fact that a topological space is a profinite space iff it is compact and totally disconnected.

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Abolfazl Tarizadeh. 2019-10-27. Ring-theoretic approaches to point-set topology. https://arxiv.org/abs/1910.12228

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