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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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## Recent Activity

Oct 21

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

## Attached Articles

## Corrections

The properties by mathcam ✓