%0 Journal Article
%T Spectral spaces and ultrafilters
%A Carmelo A. Finocchiaro
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1309.5190v1