A note on Noetherian type of spaces

Details A note on Noetherian type of spaces A note on Noetherian type of spaces

2010-03-16

arxiv.org/abs/1003.3189v1

Mathematics

General Topology

Scientific paper

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 2^{aleph_omega} by declaring the G_delta sets to be open. Milovich proved that if Square_{aleph_omega} holds and (aleph_omega)^omega=aleph_{omega+1} then Nt(X)=omega_1. Answering a question of Spadaro, we show that if (aleph_omega)^omega=aleph_{omega+1} and a strong form of Chang Conjecture holds for aleph_\omega then Nt(X)>omega_1.

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