In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874...

In mathematics, the Smith–Volterra–Cantor set (SVC), ε-Cantor set, or fat Cantor set is an example of a set of points on the real line that is nowhere...

played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one...

mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems...

In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in...

mathematics, a Cantor space, named for Georg Cantor, is a topological abstraction of the classical Cantor set: a topological space is a Cantor space if it...

when considered as subsets of the real numbers. The Cantor set is an example of an uncountable null set. It is uncountable because it contains all real numbers...

Cantor's diagonal argument (among various similar names) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence...

{\displaystyle \beth _{1}} (beth-one). The Cantor set is an uncountable subset of ⁠ R {\displaystyle \mathbb {R} } ⁠. The Cantor set is a fractal and has Hausdorff...

Cantor's first set theory article contains Georg Cantor's first theorems of transfinite set theory, which studies infinite sets and their properties....

Georg Cantor, the originator of the concept, defined cardinality as "the general concept which, with the aid of our intelligence, results from a set when...

Julia set is a Cantor space: in this case it is sometimes referred to as Fatou dust. In many cases, the Julia set of c looks like the Mandelbrot set in sufficiently...

that, in 1883, Georg Cantor, who attended lectures by Weierstrass, published examples of subsets of the real line known as Cantor sets, which had unusual...

theory of infinite sets was first developed by Georg Cantor. Although this work has become a thoroughly standard fixture of classical set theory, it has been...

meaning. The support of the Cantor distribution is the Cantor set, itself the intersection of the (countably infinitely many) sets: C 0 = [ 0 , 1 ] C 1 = [...

I.; Balasoiu, M.; Osipov, V.A. (2010). "The scattering from generalized Cantor fractals". J. Appl. Crystallogr. 43 (4): 790–7. arXiv:0911.2497. doi:10...

0 , 1 ] {\displaystyle [0,\,1]} . (The restriction of the Cantor function to the Cantor set is an example of such a function.) From it, we get a continuous...

Riemann-integrable. The function is defined by making use of the Smith–Volterra–Cantor set and an infinite number or "copies" of sections of the function defined...

{R} } ) and a meagre subset of R . {\displaystyle \mathbb {R} .} The Cantor set is nowhere dense in R {\displaystyle \mathbb {R} } and hence meagre in...

In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A {\displaystyle A} , the set of all subsets of...

development of set theory was a naive set theory. It was created at the end of the 19th century by Georg Cantor as part of his study of infinite sets and developed...

countable Cantor algebra is the Boolean algebra of all clopen subsets of the Cantor set. This is the free Boolean algebra on a countable number of generators...

measure of the set of algebraic numbers is 0, even though the set is dense in R {\displaystyle \mathbb {R} } . The Cantor set and the set of Liouville numbers...

the Smith normal form of a matrix. Smith was also first to discover the Cantor set. Smith was born in Dublin, Ireland, the fourth child of John Smith (1792–1828)...

}{\frac {b_{n}}{3^{n+1}}}} gives the Cantor function, as conventionally defined. This is one reason why the set { H , T } N {\displaystyle \{H,T\}^{\mathbb...

Schröder. It is also known as the Cantor–Bernstein theorem or Cantor–Schröder–Bernstein theorem, after Georg Cantor, who first published it (albeit without...

}{\frac {b_{n}}{3^{n+1}}}} gives the Cantor function, as conventionally defined. This is one reason why the set { H , T } N {\displaystyle \{H,T\}^{\mathbb...

(Alaoglu's theorem) The Cantor set is compact. In fact, every compact metric space is a continuous image of the Cantor set. Consider the set K of all functions...

\mathbb {R} ,} since the closure has empty interior. The Cantor set is an uncountable nowhere dense set in R . {\displaystyle \mathbb {R} .} R {\displaystyle...

considering the more general concept of restricted partial quotients. The Cantor set is a set C of measure zero from which a complete interval of real numbers...