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constant function (Definition)

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$.

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.



"constant function" is owned by mathcam. [ owner history (1) ]
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See Also: function, homotopy of maps, zero map

Other names:  constant function, constant map, constant mapping

Attachments:
constant functions and continuity (Theorem) by mathcam
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Cross-references: continuous, topological spaces, composition, function
There are 48 references to this entry.

This is version 2 of constant function, born on 2003-09-11, modified 2003-09-12.
Object id is 4727, canonical name is ConstantFunction.
Accessed 12756 times total.

Classification:
AMS MSC: 03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory )
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