For ten points, identify this group of nowhere dense perfect sets, one example of which was constructed by iteratively removing the middle third of an interval.
Babich showed that scrawny examples of these objects could not be de ned by tori in a 1992 paper. Any of these sets is, up to homeomorphism, the only totally disconnected perfect compact metric space. One example of these sets also named for Smith and Volterra has positive Lebesgue measure. The most commonly known example of these sets is also known as the ternary set and has fractal dimension less than   one, and consists of all the real numbers between zero and one whose ternary expansion never contains the digit 1. For ten points, identify this group of nowhere dense perfect sets, one example of which was constructed by iteratively removing the middle third of an interval.
Babich showed that scrawny examples of these objects could not be de ned by tori in a 1992 paper.
Cantor sets [accept Cantor comb, accept no middle third set before  middle third ]