2019/10/27 by Abolfazl Tarizadeh, Tarizadeh, Abolfazl
Mathematics · #13B10 #14A05 #54A20 #54B10 #54B99 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Commutative Algebra (math.AC) #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1910.12228
openalex publication_date 2019/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, it is shown that a topological space X is compact iff every maximal ideal of the power set ring 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.