For 10 points, identify this topologist who also names topological spaces in which any two distinct points have non-intersecting neighborhoods.
A Banach-Tarski-like paradox discovered by this person has the complement of a countable subset of the sphere divided into three congruent parts that are somehow congruent to the union of only two of the parts. This scientist showed that Zorn's lemma is equivalent to the statement that every totally ordered subset of a partially ordered set is contained in a maximal totally ordered set. A quantity discovered by this mathematician is the zero-diameter limit of the infimum of the sum of some power of the diameters of all countable covers of a set; that is his namesake measure, which is used to classify fractals. For 10 points, identify this topologist who also names topological spaces in which any two distinct points have non-intersecting neighborhoods.
A Banach-Tarski-like paradox discovered by this person has the complement of a countable subset of the sphere divided into three congruent parts that are somehow congruent to the union of only two of the parts.
Felix Hausdorff