borel class
1Borel-Moore homology — In mathematics, Borel Moore homology or homology with closed support is a homology theory for locally compact spaces. For compact spaces, the Borel Moore homology coincide with the usual singular homology, but for non compact spaces, it usually… …
2Borel set — In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are named… …
3Borel hierarchy — In mathematical logic, the Borel hierarchy is a stratification of the Borel algebra generated by the open subsets of a Polish space; elements of this algebra are called Borel sets. Each Borel set is assigned a unique countable ordinal number… …
4Borel algebra — In mathematics, the Borel algebra (or Borel sigma; algebra) on a topological space X is a sigma; algebra of subsets of X associated with the topology of X . In the mathematics literature, there are at least two nonequivalent definitions of this… …
5Borel determinacy theorem — In descriptive set theory, the Borel determinacy theorem shows that any Gale Stewart game whose winning set is a Borel set is determined, meaning that one of the two players will have a winning strategy for the game. It was proved by Donald A.… …
6Borel subgroup — In the theory of algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup. For example, in the group GLn (n x n invertible matrices), the subgroup of invertible upper… …
7Borel, Émile — ▪ French mathematician in full Félix Édouard Justin Émile born January 7, 1871, Saint Affrique, France died February 3, 1956, Paris French mathematician who created the first effective theory of the measure of sets of points and who… …
8Borel right process — Let E be a locally compact separable metric space.We will denote by mathcal E the Borel subsets of E.Let Omega be the space of right continuous maps from [0,infty) to E that have left limits in E,and for each t in [0,infty), denote by X t the… …
9Infinity-Borel set — In set theory, a subset of a Polish space X is infin; Borel if itcan be obtained by starting with the open subsets of X, and transfinitely iterating the operations of complementation and wellordered union (but see the caveat below). Formal… …
10Non-Borel set — In mathematics, a non Borel set is a set that cannot be obtained from simple sets by taking complements and at most countable unions and intersections. (For the definition see Borel set.) Only sets of real numbers are considered in this article.… …
