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A function f: R → R is bijective if and only if its graph meets every horizontal and vertical line exactly once. If X is a set, then the bijective functions from X to itself, together with the operation of functional composition (∘), form a group, the symmetric group of X, which is denoted variously by S(X), S X, or X! (X factorial).
A function is bijective if it is both injective and surjective. A bijective function is also called a bijection or a one-to-one correspondence (not to be confused with one-to-one function, which refers to injection). A function is bijective if and only if every possible image is mapped to by exactly one argument. [1]
Nowhere continuous function: is not continuous at any point of its domain; for example, the Dirichlet function. Homeomorphism: is a bijective function that is also continuous, and whose inverse is continuous. Open function: maps open sets to open sets. Closed function: maps closed sets to closed sets. Compactly supported function: vanishes ...
In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), [2] [3] also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.
The emotive [note 1] function: relates to the Addresser (sender) and is best exemplified by interjections and other sound changes that do not alter the denotative meaning of an utterance but do add information about the Addresser's (speaker's) internal state, e.g. "Wow, what a view!" Whether a person is experiencing feelings of happiness ...
An exclamative is a sentence type in English that typically expresses a feeling or emotion, but does not use one of the other structures. It often has the form as in the examples below of [WH + Complement + Subject + Verb], but can be minor sentences (i.e. without a verb) such as [WH + Complement] How wonderful!. In other words, exclamative ...
The complex exponential function mapping biholomorphically a rectangle to a quarter-annulus. In the mathematical theory of functions of one or more complex variables, and also in complex algebraic geometry, a biholomorphism or biholomorphic function is a bijective holomorphic function whose inverse is also holomorphic.
In combinatorics, bijective proof is a proof technique for proving that two sets have equally many elements, or that the sets in two combinatorial classes have equal size, by finding a bijective function that maps one set one-to-one onto the other. This technique can be useful as a way of finding a formula for the number of elements of certain ...