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# constant function

Definition Suppose $X$ and $Y$ are sets and $f:X\to Y$ is a function. Then $f$ is a constant function if $f(a)=f(b)$ for all $a,b$ in $X$.

# 0.0.1 Properties

1. The composition of a constant function with any function (for which composition is defined) is a constant function.

2. A constant map between topological spaces is continuous.

Related:

Function,HomotopyOfMaps, ZeroMap

Synonym:

constant function,constant map, constant mapping

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

03E20*no label found*

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new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

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new question: Prove a formula is part of the Gentzen System by LadyAnne

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new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

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The properties by mathcam ✓