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Equivariant cohomology. In mathematics, equivariant cohomology (or Borel cohomology) is a cohomology theory from algebraic topology which applies to topological spaces with a group action. It can be viewed as a common generalization of group cohomology and an ordinary cohomology theory. Specifically, the equivariant cohomology ring of a space ...
Borel subgroups are one of the two key ingredients in understanding the structure of simple (more generally, reductive) algebraic groups, in Jacques Tits ' theory of groups with a ( B, N) pair. Here the group B is a Borel subgroup and N is the normalizer of a maximal torus contained in B . The notion was introduced by Armand Borel, who played a ...
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 called the rank of the Borel set. The Borel hierarchy is of particular interest in descriptive set theory .
Borel 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 after Émile Borel . For a topological space X, the collection of all Borel sets on X ...
Looping in education is the practice of moving groups of children up from one grade to the next with the same teacher. [1] For example, a teacher who teaches a third grade class and then goes on to teach the same students, the following year, for the fourth grade. This system, which is also called multiyear grouping, [2] lasts from two to five ...
Brian Hernandez Jr. went back to his roots to make history in Kentucky Derby 150. Having drawn Post 3 with Mystik Dan, the 38-year-old jockey broke out the tape of Calvin Borel's victories riding ...
Borel–Cantelli lemma. In probability theory, the Borel–Cantelli lemma is a theorem about sequences of events. In general, it is a result in measure theory. It is named after Émile Borel and Francesco Paolo Cantelli, who gave statement to the lemma in the first decades of the 20th century. [1] [2] A related result, sometimes called the ...
A Borel measure is any measure defined on the σ-algebra of Borel sets. [2] A few authors require in addition that is locally finite, meaning that for every compact set . If a Borel measure is both inner regular and outer regular, it is called a regular Borel measure. If is both inner regular, outer regular, and locally finite, it is called a ...