Projective limits of topological spaces III: finishing the proof of Steenrod’s theorem

Last time, we embarked on proving that the projective limit of a projective system of compact sober (resp., and non-empty) spaces is compact and sober (resp., and non-empty), a theorem that Fujiwara and Kato call Steenrod’s Theorem.  However, instead, we merely proved that a projective limit of a projective system of non-empty compact sober spaces is non-empty.  Do not despair: this is the essential argument in the proof of Steenrod’s Theorem, which we complete this month.  Read the full post.


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