A note on Noetherian type of spaces
Abstract
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 alephω then Nt(X)>omega1.
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