In mathematics, the Iwahori – Hecke algebra, or Hecke algebra, named for Erich Hecke and Nagayoshi Iwahori, is a one-parameter deformation of the group algebra of a Coxeter group.

* A reductive algebraic group over a local field has a BN-pair where B is an Iwahori subgroup.

* 1983 – Jun Matsumoto, Japanese singer, dancer, and actor ( Arashi )

* 1954 – Jack Blades, American musician ( Night Ranger, Rubicon, Damn Yankees, and Tak Matsumoto Group )

* 1964 – Hideto " hide " Matsumoto, Japanese musician ( X Japan ) ( d. 1998 )

* 1938 – Leiji Matsumoto, Japanese author

In a 2003 presentation at an open source convention, Yukihiro Matsumoto, creator of the programming language Ruby, said that one of his inspirations for developing the language was the science fiction novel Babel-17, based on the Sapir – Whorf Hypothesis.

* 1963 – Hitoshi Matsumoto, Japanese comedian

* December 13 – Hideto " hide " Matsumoto, Japanese musician

* November 30 – Rica Matsumoto, Japanese voice actress and singer

* March 27 – Tak Matsumoto, Japanese guitarist ( B ' z )

* August 4 – Seichō Matsumoto, Japanese writer and journalist ( b. 1909 )

* Yasunori Matsumoto – seiyu voice actor

* Kiyoshi Matsumoto – politician, founder of major drug store chain

* Tetsuya Matsumoto – professional baseball player

* Mirai ( 2003 ) – album by Yusuke Matsumoto

* Tomoyo ( 松本知世 Matsumoto Tomoyo, born March 2, 1987 ) – Timbales, current leader

* Hideto Matsumoto ( 1964 – 1998 ), better known as hide, musician

* Katsuji Matsumoto ( 1904 – 1986 ), illustrator and manga author

* Seichō Matsumoto ( 1909 – 1992 ), author

* Matsumoto Takashi ( 1906 – 1956 ), writer

* Leo Matsumoto – actress

* Matsumoto Kōshirō IX ( October 1981 – present )-Son of Kōshirō VIII.

# " All for You " ( Natsumi Watanabe, Ryoki Matsumoto ) – 6: 00

* Borel – Weil theorem

That this form of compactness holds for closed and bounded subsets of Euclidean space is known as the Heine – Borel theorem.

The Heine – Borel theorem, as the result is now known, is another special property possessed by closed and bounded sets of real numbers.

Ultimately the Russian school of point-set topology, under the direction of Pavel Alexandrov and Pavel Urysohn, formulated Heine – Borel compactness in a way that could be applied to the modern notion of a topological space.

This follows from the Heine – Borel theorem.

Again from the Heine – Borel theorem, the closed unit ball of any finite-dimensional normed vector space is compact.

# A is closed and bounded ( Heine – Borel theorem ).

This is a generalization of the Heine – Borel theorem, which states that any closed and bounded subspace S of R < sup > n </ sup > is compact and therefore complete.

* 1871 – Émile Borel, French mathematician and politician ( d. 1956 )

In the 1940s – 1950s, Ellis Kolchin, Armand Borel and Claude Chevalley realised that many foundational results concerning Lie groups can be developed completely algebraically, giving rise to the theory of algebraic groups defined over an arbitrary field.

Classical measure theory makes deep usage of the axiom of choice, which is fundamental to, first, distinction between measurable and non-measurable sets, the existence of the latter being behind such famous results as the Banach – Tarski paradox, and secondly the hierarchies of notions of measure captured by notions such as Borel algebras, which are an important source of intuitions in set theory.

* 1966 – Calvin Borel, American horse jockey

Nevanlinna gave a fuller account of the theory in the monographs La théoreme de Picard – Borel et la théorie des fonctions méromorphes ( 1929 ) and Eindeutige analytische Funktionen ( 1936 ).

Important results include the Bolzano – Weierstrass and Heine – Borel theorems, the intermediate value theorem and mean value theorem, the fundamental theorem of calculus, and the monotone convergence theorem.

The Heine – Borel theorem implies that a Euclidean n-sphere is compact.

* January 7 – Félix Édouard Justin Émile Borel, French mathematician and politician ( d. 1956 )

Both follow easily from the second Borel – Cantelli lemma.

In probability theory, the Borel – Cantelli lemma is a theorem about sequences of events.

A related result, sometimes called the second Borel – Cantelli lemma, is a partial converse of the first Borel – Cantelli lemma.

The Borel – Cantelli lemma states:

* The Euclidean spaces R < sup >< var > n </ var ></ sup > ( and in particular the real line R ) are locally compact as a consequence of the Heine – Borel theorem.