Abstract
In this article, we introduce new topologies on the prime spectrum of a commutative ring by using the ℱ-limit of a sequence of prime ideals where ℱ is a nonprincipal ultrafilter on the natural numbers ℕ. These topologies are strictly finer than the Zariski's Topology, countably compact and Hausdorff. We construct 2𝔠 new topologies on Spec(ℚℕ) which are pairwise non-homeomorphic.
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