\section{Combination Theorem for Continuous Mappings/Topological Ring/Combined Rule}
Tags: Continuous Functions

\begin{theorem}
:$\lambda * f + \mu * g: \struct{S, \tau_{_S}} \to \struct{R, \tau_{_R}}$ is a [[Definition:Continuous Mapping on Set|continuous mapping]]
:$f * \lambda + g * \mu: \struct{S, \tau_{_S}} \to \struct{R, \tau_{_R}}$ is a [[Definition:Continuous Mapping on Set|continuous mapping]].
\end{theorem}

\begin{proof}
{{ProofWanted}}
[[Category:Continuous Functions]]
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\end{proof}


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