quasi wrote: >William Elliot wrote: >> >>Can an uncountable compact Hausdorff be continuously mapped >>onto [0,1]? > >This has already been answered by David Ullrich (with >improvements Butch Malahide)
Sorry -- I hit post button too early.
A followup question.
Prove or disprove:
If X is a topological space and f: X -> [0,1] is a continuous surjection, then X has a subspace homeomorphic to the Cantor set.