2013/03/11 by Tomoki Mihara, Mihara, Tomoki
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Logic (math.LO) #Number Theory (math.NT) #Topological and Geometric Data Analysis #advanced mathematical theories #math.FA #math.GN #math.LO #math.NT
paper · pdf · doi:10.48550/arxiv.1303.2435
19 pages
arxiv created 2013/03/11 · openalex publication_date 2013/03/11 · arxiv updated 2013/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We verified that the existence of a maximal ideal of height 0 in a p-adic algebra in a certain class is independent of the axiom of ZFC. We established the theory on a P-point in the boundary of a topological space in the universal totally disconnected Hausdorff compactification. It is quite similar with the theory on a P-point in the boundary of a topological space in the Stone-Cech compactification. The latter theory relies on the real analysis, and the reason why the real analysis works for it is because the Stone-Cech compactification has the lifting property for a real bounded continuous function. On the other hand, the universal totally disconnected Hausdorff compactification does not have the lifting property for a real bounded continuous function in general, and hence the same technique with the real analysis is not valid for the former theory. We applied the p-adic analysis instead, and it yields a relation with a P-point in the boundary in the universal totally disconnected Hausdorff compactification and a maximal ideal of height 0 in the corresponding p-adic algebra.