In mathematics, a partition of unity of a topological spaceX is a set of continuous functions {ρi} from X to the unit interval [0,1] such that every point has a neighbourhood where all but a finite number of the functions are identically zero, and the sum of all the functions on the entire space is identically 1, Main article: History of mathematics The evolution of mathematics can be seen to be an ever increasing series of abstractions. ... Topological spaces are structures that allow one to formalize concepts such as convergence, connectedness and continuity. ... In topology, a continuous function is generally defined as one for which preimages of open sets are open. ... In mathematics, the unit interval is the interval [0,1], that is the set of all real numbers x such that zero is less than or equal to x and x is less than or equal to one. ... This is a glossary of some terms used in the branch of mathematics known as topology. ... In mathematics, a set is called finite if and only if there is a bijection between the set and some set of the form {1, 2, ..., n} where is a natural number. ...
Partitions of unity are useful because they often allow one to extend local constructions to the whole space.
See also: paracompact space In mathematics, a paracompact space is a topological space in which every open cover admits an open locally finite refinement. ...
The partition of India refers to the creation in August 1947 of two sovereign states of India and Pakistan when Britain granted independence to the former British Raj including treaty states.
The seeds of partition were sown long before independence, in the struggle between various factions of the Indian nationalist movement, and especially of the Indian National Congress, for control of the movement.
The Partition was a highly controversial arrangement, and remains a cause of much tension on the Subcontinent today.
Feeds |
Contact