Implications

We have the following indirect implication of form equivalence classes:

106 \(\Rightarrow\) 78
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
106 \(\Rightarrow\) 78 Injectivity, projectivity and the axiom of choice, Blass, A. 1979, Trans. Amer. Math. Soc.

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

Howard-Rubin Number Statement
106:

Baire Category Theorem for Compact Hausdorff Spaces: Every compact Hausdorff space is Baire.

78:

Urysohn's Lemma:  If \(A\) and \(B\) are disjoint closed sets in a normal space \(S\), then there is a continuous \(f:S\rightarrow [0,1]\) which is 1 everywhere in \(A\) and 0 everywhere in \(B\). Urysohn [1925], pp 290-292.

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