A note on Noetherian type of spaces
Soukup, Lajos
الأصل · EN
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.
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