Combination Theorem for Continuous Mappings/Topological Ring/Combined Rule

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Theorem

Let $\struct{S, \tau_S}$ be a topological space.

Let $\struct{R, +, *, \tau_R}$ be a topological ring.


Let $\lambda, \mu \in R$ be arbitrary element in $R$.

Let $f,g : \struct{S, \tau_S} \to \struct{R, \tau_R}$ be continuous mappings.


Then


Proof

$\blacksquare$