Order / Lattice Theory (?): The Boolean Prime Ideal Theorem (BPI). It is strictly weaker than the axiom of choice but equivalent(!) equivalent to Tychonovs theorem (EDIT: of course the version where the spaces are Hausdorff, compact) therefore underlying all of functional analysis.
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Order / Lattice Theory (?): The Boolean Prime Ideal Theorem (BPI). It is strictly weaker than the axiom of choice but equivalent(!) to Tychonovs theorem therefore underlying all of functional analysis. |
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