bolzano-weierstrass theorem
1Bolzano–Weierstrass theorem — In real analysis, the Bolzano–Weierstrass theorem is a fundamental result about convergence in a finite dimensional Euclidean space R^n. The theorem states that each bounded sequence in R^n has a convergent subsequence. An equivalent formulation… …
2Bolzano-Weierstrass theorem — /bohl zah noh vuy euhr shtrahs , strahs , bohlt sah /, Math. the theorem that every bounded set with an infinite number of elements contains at least one accumulation point. [named after B. BOLZANO and K. Weierstrass (1815 97), German… …
3Bolzano-Weierstrass theorem — /bohl zah noh vuy euhr shtrahs , strahs , bohlt sah /, Math. the theorem that every bounded set with an infinite number of elements contains at least one accumulation point. [named after B. BOLZANO and K. Weierstrass (1815 97), German… …
4Weierstrass theorem — Several theorems are named after Karl Weierstrass. These include: *The Weierstrass approximation theorem, also known as the Stone Weierstrauss theorem *The Bolzano Weierstrass theorem, which ensures compactness of closed and bounded sets in R n… …
5Extreme value theorem — This article is about continuous functions in analysis. For statistical theorems about the largest observation in a sequence of random variables, see extreme value theory. A continuous function ƒ(x) on the closed interval [a,b] showing the… …
6Karl Weierstrass — Infobox Scientist name = Karl Weierstrass |300px caption = Karl Theodor Wilhelm Weierstrass (Weierstraß) birth date = birth date|1815|10|31|mf=y birth place = Ostenfelde, Westphalia death date = death date and age|1897|2|19|1815|10|31|mf=y death… …
7Bernard Bolzano — Bernard (Bernhard) Placidus Johann Nepomuk Bolzano (birth date|1781|10|5|mf=y ndash; December 18, 1848) was a Bohemian mathematician, theologian, philosopher, logician and antimilitarist of German mother tongue.FamilyBolzano was the son of two… …
8Weierstrass function — may also refer to the Weierstrass elliptic function ( ) or the Weierstrass sigma, zeta, or eta functions. Plot of Weierstrass Function over the interval [−2, 2]. Like fractals, the function exhibits self similarity: every zoom (red circle)… …
9Heine–Borel theorem — In the topology of metric spaces the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states:For a subset S of Euclidean space R n , the following two statements are equivalent: * S is closed and bounded *every open cover of S has a …
10Kakutani fixed point theorem — In mathematical analysis, the Kakutani fixed point theorem is a fixed point theorem for set valued functions. It provides sufficient conditions for a set valued function defined on a convex, compact subset of a Euclidean space to have a fixed… …
