query: Proving the claim that the Cantor set $C$ is perfect
positive_passages.docid: 151686
positive_passages.text: A proof that the Cantor set is Perfect
negative_passages.docid: 54761
negative_passages.text: Inverting the Cantor pairing function
negative_passages.docid: 114770
negative_passages.text: Proof that a perfect set is uncountable
negative_passages.docid: 26563
negative_passages.text: Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
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: 92588
negative_passages.text: Showing that $(C_0([0,\infty)), \|\cdot\|_\infty)$ is complete.
negative_passages.docid: 11395
negative_passages.text: Why is the Cantor function not absolutely continuous?
negative_passages.docid: 47016
negative_passages.text: Riemann integral of characteristic function of Cantor set
negative_passages.docid: 133086
negative_passages.text: When Cantor's Intersection theorem won't work with closed sets
negative_passages.docid: 128437
negative_passages.text: How to prove that a finite set is countable
negative_passages.docid: 12436
negative_passages.text: The cardinality of the set of all finite subsets of an infinite set
negative_passages.docid: 4912
negative_passages.text: Show that an infinite set $C$ is equipotent to its cartesian product $C\times C$
negative_passages.docid: 132046
negative_passages.text: Looking for Cantor's original proof of the Cantor-Bernstein theorem that relies on the axiom of choice?
negative_passages.docid: 144787
negative_passages.text: Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
negative_passages.docid: 48727
negative_passages.text: Why is the Cantor set not defined by a limit?
negative_passages.docid: 95947
negative_passages.text: Cantor set + Cantor set =$[0,2]$
negative_passages.docid: 79974
negative_passages.text: The cardinality of Lebesgue sets