Kuratowski's closure-complement problem
- Kuratowski's closure-complement problem
In the mathematical subject of topology, Kuratowski's closure-complement problem refers to the statement that at most 14 distinct sets can be obtained by repeatedly applying the set operations of closure and complement to a given starting subset of a topological space. This result was first published by Kazimierz Kuratowski in 1922. Many variations have appeared since, especially after 1960.
A subset realizing the maximum of 14 is called a 14-set. The real numbers have subsets that are 14-sets.
References
1. Kelley, J. L. General Topology. Princeton: Van Nostrand, p. 57, 1955.
2. Kuratowski, K. Sur l'operation A de l'analysis situs. Fund. Math. 3, 182-199, 1922.
External links
* [http://www.latrobe.edu.au/mathstats/maths/department/algebra-research-group/Papers/GJ_Kuratowski.pdf The Kuratowski Closure-Complement Problem] by B.J. Gardner and Marcel Jackson
Wikimedia Foundation.
2010.
Look at other dictionaries:
Kazimierz Kuratowski — TOCleftKazimierz Kuratowski (Warsaw, February 2, 1896 ndash;June 18, 1980) was a Polish mathematician and logician.BiographyKuratowski was born a subject of Tsarist Russia. In 1913, he enrolled in an engineering course at the University of… … Wikipedia
List of mathematics articles (K) — NOTOC K K approximation of k hitting set K ary tree K core K edge connected graph K equivalence K factor error K finite K function K homology K means algorithm K medoids K minimum spanning tree K Poincaré algebra K Poincaré group K set (geometry) … Wikipedia
14 (number) — ← 13 15 → 14 ← 10 11 12 13 14 15 16 … Wikipedia
14 (nombre) — Cet article est une page généraliste sur le nombre 14, le numéro 14, et le mot 14. Pour l année, voir 14. 14 Cardinal Quatorze Ordinal quatorzième 14e Préfixe grec … Wikipédia en Français
Matroid — In combinatorics, a branch of mathematics, a matroid ( /ˈmeɪ … Wikipedia
List of mathematics articles (T) — NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie … Wikipedia
Metric space — In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3 dimensional Euclidean… … Wikipedia