Locally constant function

In mathematics, a function from a topological space into a set is called locally constant if for every one around there, on the constant.

Properties

Every constant function is locally constant.
Every locally constant function of any in a set is constant, as coherently and is not to cover by at least two disjoint open sets.
Every locally constant holomorphic function of an open set in the complex numbers is constant, if an area is, so is connected.
In general, any locally constant function is constant on each connected component, for locally connected spaces converse is also true.
An illustration of a topological space to a discrete space is continuous if it is locally constant.
Each illustration of a discrete space in any topological space is locally constant.
The amount of locally constant functions on a space naturally form a sheaf of commutative rings.

The function defined by for and is locally constant. (This one goes that is irrational, because so and are open sets that cover. )
The function defined by for and is as locally constant.
The sign function is not locally constant.
Step functions are not local, but piecewise constant

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