A note on Noetherian type of spaces
General Topology
2010-03-17 v1 Logic
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 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.
Keywords
Cite
@article{arxiv.1003.3189,
title = {A note on Noetherian type of spaces},
author = {Lajos Soukup},
journal= {arXiv preprint arXiv:1003.3189},
year = {2010}
}