Cantor set

Noun

Meaning

English Wikipedia has an article on:Cantor setWikipedia
construction of the Cantor set
Cantor set (plural Cantor sets)

(mathematical analysis, topology) A subset of an interval formed by recursively removing an interval in the middle of every connected component of the set.

Source: en.wiktionary.org

Synonyms

Cantor dust

Examples

A column capital from the Ancient Egyptian site of the island of Philae carries a pattern which resembles the Cantor set. Source: Internet

A subset of the Cantor set which is not Borel measurable The Borel measure is not complete. Source: Internet

Every point of the Cantor set is also an accumulation point of the complement of the Cantor set. Source: Internet

For any point in the Cantor set and any arbitrarily small neighborhood of the point, there is some other number with a ternary numeral of only 0s and 2s, as well as numbers whose ternary numerals contain 1s. Source: Internet

However, the set of endpoints of the removed intervals is countable, so there must be uncountably many numbers in the Cantor set which are not interval endpoints. Source: Internet

In fact, every compact metric space is a continuous image of the Cantor set. Source: Internet

Close letter words and terms

Cantopop cantor Cantor dust cantor's set theory Cantor-Bendixson theorem cantoral