constant functionConstantFunction2003-09-11 17:51:372003-09-12 03:10:58Definition% this is the default PlanetMath preamble. as your knowledge
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\makeatother{\bf Definition} Suppose $X$ and $Y$ are sets and $f:X\to Y$ is a function.
Then $f$ is a {\bf constant function} if $f(a) = f(b)$ for all $a,b$
in $X$.
\subsubsection{Properties}
\begin{enumerate}
\item The composition of a constant function
with any function (for which composition is defined) is a constant function.
\item A constant map between topological spaces is continuous.
\end{enumerate}