In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about convex sets in topological vector spaces. A particular case of this theorem, which can be easily visualized, states that given a convex polygon, one only needs the corners of the polygon to recover the polygon shape. The statement of the theorem is false if the polygon is not convex, as then there can be many ways of drawing a polygon having given points as corners. Formally, let be a locally convex topological vector space (assumed to be Hausdorff), and let be a compact convex subset of . Then, the theorem states that is the closed convex hull of its extreme points. The closed convex hull above is defined as the intersection of all closed convex subsets of that contain This turns out to be the same as the closure of the convex hull in the topological vector space. One direction in the theorem is easy; the main burden is to show that there are 'enough' extreme points. The original statement proved by Mark Krein and David Milman was somewhat less general than this. Hermann Minkowski had already proved that if is 3-dimensional then equals the convex hull of the set of its extreme points. This assertion was expanded to the case of any finite dimension by Ernst Steinitz. The Krein–Milman theorem generalizes this to arbitrary locally convex , with a caveat: the closure may be needed.

Bal Mithai (Hindi: बाल मिठाई) is a brown chocolate-like fudge, made with roasted khoa, coated with white sugar balls, and is a popular sweet from Almora in the Himalayan state of Uttarakhand in India, especially regions around Almora.It is one of the most favourite sweet of common people and the people living near almora region. But now in some places artificial or fake sweets are also made up to fool tourists and selled on much higher price too

André Cassagnes (September 23, 1926 – January 16, 2013) was a French inventor, electrical technician, toymaker, and kite designer. Cassagnes is best known as the inventor of the Etch A Sketch, a popular mechanical drawing toy manufactured since 2016 by Spin Master, formerly by the Ohio Art Company. Cassagnes was born outside Paris, France, on September 23, 1926. His parents owned and operated a bakery, where he worked as a teenager. An allergy to flour forced him to seek another line of work, and he became an electrician for the Lincrusta Company, a French manufacturer which produced picture frame covers using an aluminum powder. In one instance, Cassagnes was performing a routine installation of a factory light switch plate. The plate was wrapped in a translucent decal covering. During the installation, Cassagnes removed the decal and wrote on it with a pencil. He quickly noticed that image transferred to the opposite face of the decal. Cassagnes tinkered with his discovery, which led to the world's first prototype of the Etch A Sketch. He called his invention L'Ecran Magique, which is translated as "the Magic Screen." The toy was first unveiled in 1959 at the Nuremberg Toy Fair in Nuremberg, West Germany. Cassagnes later partnered with the American manufacturer Ohio Art Company to further develop the Etch a Sketch into its familiar form. The Ohio Art Company launched the Etch a Sketch in the United States during the 1960 holiday season. Cassagnes was also a well known kite designer and inventor in France. This was his main occupation but remained a hobby; he specialized in the creation of original modular kites throughout the 1980s. A 1992 article in Kite Lines magazine described him then as "the most famous kitemaker in France." He also invented several mechanical games: the Teleguide, which guides metal cars onto a track; and the SkeDoodle, a conceptual toy in which users draw images onto a globe-shaped screen. Cassagnes died in a suburb of Paris on January 16, 2013, at the age of 86, according to a report from the Toy Industry Association (TIA). He lived with his wife, Renée, and their three children.

In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about convex sets in topological vector spaces. A particular case of this theorem, which can be easily visualized, states that given a convex polygon, one only needs the corners of the polygon to recover the polygon shape. The statement of the theorem is false if the polygon is not convex, as then there can be many ways of drawing a polygon having given points as corners. The original statement proved by Mark Krein and David Milman was somewhat less general than this.

A Suitable Boy is a drama miniseries written by Andrew Davies, adapted from the novel of the same name by Vikram Seth. The drama directed by Mira Nair and starring Tabu, Ishaan Khatter, , Rasika Dugal, and Ram Kapoor follows the story of spirited university student Lata (played by Tanya Maniktala), coming of age in North India in 1951. The filming of the series began in September 2019 in Lucknow. The first episode is due to be aired on 26 July on BBC One.

Alles (disambiguation)

André Cassagnes (September 23, 1926 – January 16, 2013) was a French inventor, electrical technician, toymaker, and kite designer. Cassagnes is best known as the inventor of the Etch A Sketch, a popular mechanical drawing toy manufactured since 2016 by Spin Master, formerly by the Ohio Art Company. Cassagnes died in a suburb of Paris on January 16, 2013, at the age of 86, according to a report from the Toy Industry Association (TIA). He lived with his wife, Renée, and their three children.