query: Hausdorff dimension of a Cantor set.
positive_passages.docid: 93389
positive_passages.text: Uncountable sets of Hausdorff dimension zero
negative_passages.docid: 128934
negative_passages.text: Every infinite Hausdorff space has an infinite discrete subspace
negative_passages.docid: 136094
negative_passages.text: $G_\delta$ singletons in compact Hausdorff and first countability
negative_passages.docid: 154240
negative_passages.text: Inverse of Heine–Cantor theorem
negative_passages.docid: 23442
negative_passages.text: Cardinality of the union of infinite and countable sets
negative_passages.docid: 115173
negative_passages.text: The Cantor set is homeomorphic to infinite product of $\{0,1\}$ with itself - cylinder basis - and it topology
negative_passages.docid: 19289
negative_passages.text: complement of a set and its measure
negative_passages.docid: 69534
negative_passages.text: Measure of the Cantor set plus the Cantor set
negative_passages.docid: 133938
negative_passages.text: Connectedness of the Hausdorff distance.
negative_passages.docid: 113227
negative_passages.text: Measure spaces are proper subsets
negative_passages.docid: 66239
negative_passages.text: Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
negative_passages.docid: 14048
negative_passages.text: Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
negative_passages.docid: 69273
negative_passages.text: Is there a compact subset of the irrationals with positive Lebesgue measure?
negative_passages.docid: 3023
negative_passages.text: Construction of a Borel set with positive but not full measure in each interval
negative_passages.docid: 136795
negative_passages.text: A non-measurable set of given outer measure
negative_passages.docid: 146062
negative_passages.text: A "Cantor-Schroder-Bernstein" theorem for partially-ordered-sets
negative_passages.docid: 49039
negative_passages.text: Sets with Hausdorff-Measure 0