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A diagram is worth a thousand words.

Taken from the beautiful book by Herrlich, Axiom of choice, Lecture Notes in Mathematics 1876, Springer 2006. Most of the implications are one-way implications, i.e., known to be not reversible:

Herrlich's diagram

http://i.stack.imgur.com/4KMFB.png

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A diagram is worth a thousand words.

Taken from the beautiful book by Herrlich, Axiom of choice, Lecture Notes in Mathematics 1876, Springer 2006. Most of the implications are one-way implications, i.e., known to be not reversible:

Herrlich's diagram