Mathematics – General Topology
Scientific paper
2010-12-17
Mathematics
General Topology
20 pages
Scientific paper
We study some cardinal invariants of an order-theoretic fashion on products and box products of topological spaces. In particular, we concentrate on the Noetherian type (Nt), defined by Peregudov in the 1990s. Some highlights of our results include: 1) There are spaces $X$ and $Y$ such that $Nt(X \times Y) < \min\{Nt(X), Nt(Y)\}$. 2) In several classes of compact spaces, the Noetherian type is preserved by their square and their dense subspaces. 3) The Noetherian type of some countably supported box products cannot be determined in ZFC. In particular, it is sensitive to square principles and some Chang Conjecture variants. 4) PCF theory can be used to provide ZFC upper bounds to Noetherian type on countably supported box products. The underlying combinatorial notion is a weakening of Shelah's freeness.
Kojman Menachem
Milovich David
Spadaro Santi
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