Combination Theorem for Continuous Mappings/Topological Group

Theorem
Let $\struct {S, \tau_{_S} }$ be a topological space.

Let $\struct {G, *, \tau_{_G} }$ be a topological group.

Let $\lambda \in G$.

Let $f, g : \struct {S, \tau_{_S} } \to \struct {G, \tau_{_G} }$ be continuous mappings.

Then the following results hold:

Also see

 * Combination Theorem for Continuous Mappings to Topological Semigroup