Implications

We have the following indirect implication of form equivalence classes:

386 \(\Rightarrow\) 249
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
386 \(\Rightarrow\) 10 Products, the Baire category theorem, and the axiom of dependent choice, Herrlich-Keremedis-1999a[1999a], Topology and its Applications.
10 \(\Rightarrow\) 249

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
386:

Every B compact (pseudo)metric space is Baire.

10:

\(C(\aleph_{0},< \aleph_{0})\):  Every denumerable family of non-empty finite sets has a choice function.

249:

If \(T\) is an infinite tree in which every element has exactly 2 immediate successors then \(T\) has an infinite branch.

Comment:

Back