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In real analysis the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states: For a subset S of Euclidean space Rn, the following two statements...

In topology, a branch of mathematics, Borel's theorem, due to Armand Borel (1953), says the cohomology ring of a classifying space or a classifying stack...

lemma Borel's law of large numbers Borel measure Borel–Kolmogorov paradox Borel–Cantelli lemma Borel–Carathéodory theorem Heine–Borel theorem Borel determinacy...

In mathematics, the Borel–Weil–Bott theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can...

In mathematics, the Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application...

In descriptive set theory, the Borel determinacy theorem states that any Gale–Stewart game whose payoff set is a Borel set is determined, meaning that...

In mathematics, Borel's lemma, named after Émile Borel, is an important result used in the theory of asymptotic expansions and partial differential equations...

Borel (1895), and it was generalized to arbitrary collections of intervals by Pierre Cousin (1895) and Henri Lebesgue (1904). The Heine–Borel theorem...

Borel fixed-point theorem is a fixed-point theorem in algebraic geometry generalizing the Lie–Kolchin theorem. The result was proved by Armand Borel (1956)...

as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth...

as the intermediate value theorem, the Bolzano–Weierstrass theorem, the extreme value theorem, and the Heine–Borel theorem. It is usually taken as an...

{\displaystyle A_{n}(z)=\sum _{k=0}^{n}a_{k}z^{k}.} A weak form of Borel's summation method defines the Borel sum of A to be lim t → ∞ e − t ∑ n = 0 ∞ t n n ! A n (...

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...

In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result...

Then X as a Borel space is isomorphic to one of R, Z, a finite space. (This result is reminiscent of Maharam's theorem.) Considered as Borel spaces, the...

analysis, the Borel graph theorem is generalization of the closed graph theorem that was proven by L. Schwartz. The Borel graph theorem shows that the...

the Borel measure described above). This idea extends to finite-dimensional spaces R n {\displaystyle \mathbb {R} ^{n}} (the Cramér–Wold theorem, below)...

they have the same Markov constant. As said above, the constant in Borel's theorem may not be improved, as shown by Adolf Hurwitz in 1891. Let ϕ = 1 +...

In mathematics, the Baily–Borel compactification is a compactification of a quotient of a Hermitian symmetric space by an arithmetic group, introduced...

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type...