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- Locally_constant_function abstract "In mathematics, a function f from a topological space A to a set B is called locally constant, if for every a in A there exists a neighborhood U of a, such that f is constant on U.Every constant function is locally constant.Every locally constant function from the real numbers R to R is constant by the connectedness of R. But the function f from the rationals Q to R, defined by f(x) = 0 for x < π, and f(x) = 1 for x > π, is locally constant (here we use the fact that π is irrational and that therefore the two sets {x∈Q : x < π} and {x∈Q : x > π} are both open in Q).If f : A → B is locally constant, then it is constant on any connected component of A. The converse is true for locally connected spaces (where the connected components are open).Further examples include the following: Given a covering p : C → X, then to each point x of X we can assign the cardinality of the fiber p−1(x) over x; this assignment is locally constant. A map from a topological space A to a discrete space B is continuous if and only if it is locally constant.".
- Locally_constant_function wikiPageID "295629".
- Locally_constant_function wikiPageRevisionID "586565390".
- Locally_constant_function hasPhotoCollection Locally_constant_function.
- Locally_constant_function subject Category:Sheaf_theory.
- Locally_constant_function comment "In mathematics, a function f from a topological space A to a set B is called locally constant, if for every a in A there exists a neighborhood U of a, such that f is constant on U.Every constant function is locally constant.Every locally constant function from the real numbers R to R is constant by the connectedness of R.".
- Locally_constant_function label "Locally constant function".
- Locally_constant_function label "Lokal konstante Funktion".
- Locally_constant_function sameAs Lokal_konstante_Funktion.
- Locally_constant_function sameAs m.01r660.
- Locally_constant_function sameAs Q1762213.
- Locally_constant_function sameAs Q1762213.
- Locally_constant_function wasDerivedFrom Locally_constant_function?oldid=586565390.
- Locally_constant_function isPrimaryTopicOf Locally_constant_function.