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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

2 votes

Is a certain subset of the disc a convex set?

Start with a 3 point set {a,b,c} on the unit circle. The union of the 3 chords forms not a convex set. Blow up the points into 3 very small Cantor sets. The union of all the new chords still fails mis …
Paul Fabel's user avatar
  • 1,968
5 votes

Inserting an open and simply-connected set between a compact set and an open set

Perhaps the theorem at the common intersection of the various ambiguous interpretations of the inquiry at hand is the following: If the planar open set U contains a continuum K and if the planar com …
Paul Fabel's user avatar
  • 1,968