Combination Theorem for Continuous Mappings/Topological Ring/Combined Rule

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