2010/03/16 by Lajos Soukup, Soukup, Lajos
Decision Sciences · Mathematics · #03E35 #54A25 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.1003.3189
openalex publication_date 2010/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Noetherian type of a space X, Nt(X), is the least cardinal kappa such that X has a base B such that every element of the base is contained in less than kappa many elements of the base. Denote X the space obtained from 2alephomega by declaring the Gdelta sets to be open. Milovich proved that if Squarealephomega holds and (alephomega)omega=alephomega+1 then Nt(X)=omega1. Answering a question of Spadaro, we show that if (alephomega)omega=alephomega+1 and a strong form of Chang Conjecture holds for alephωthen Nt(X)>omega1.