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arXiv · 1309.5190

Spectral spaces and ultrafilters

Carmelo A. Finocchiaro
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Abstract

Let $X$ be the prime spectrum of a ring. In [arXiv:0707.1525] the authors define a topology on $X$ by using ultrafilters and they show that this topology is precisely the constructible topology. In this paper we generalize the construction given in [arXiv:0707.1525] and, starting from a set $X$ and a collection of subsets $\mathcal{F}$ of $X$, we define by using ultrafilters a topology on $X$ in which $\mathcal F$ is a collection of clopen sets. We use this construction for giving a new characterization of spectral spaces and several new examples of spectral spaces.

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Carmelo A. Finocchiaro. 2013-09-20. Spectral spaces and ultrafilters. https://arxiv.org/abs/1309.5190

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