The theorem stating that, in a certain kind of space, a set of pointwise bounded linear operators is uniformly bounded is named for him and Hugo Steinhaus.
One theorem named for this man can be proven by iteratively applying a function, then bounding above by a geometric sequence to show that those points are Cauchy convergent. Along with an alliteratively named Austrian, this man lends his name to a theorem allowing the extension of a sublinear functional to a whole space. If a self-map T in a metric space has the property that the distance between Tx and Ty is less than a subunitary constant times the distance between x and y, then T has a (*) fixed point, according to his theorem about contraction mappings. The theorem stating that, in a certain kind of space, a set of pointwise bounded linear operators is uniformly bounded is named for him and Hugo Steinhaus. This man's namesake spaces are complete normed vector spaces. For 10 points, identify this Polish mathematician who co-names a result that uses the axiom of choice to cut up a sphere and reassemble it into two identical copies, along with Tarski.
One theorem named for this man can be proven by iteratively applying a function, then bounding above by a geometric sequence to show that those points are Cauchy convergent.
Stefan Banach