How to prove the induced map; $g_* : C(Y) \rightarrow C(X)$, induced from the map $g \in C(X, Y)$, endowed with fine topology is an embedding.
How to prove the continuity of an induced map; $g_* : C(X, Y) \rightarrow C(X, R)$, induced from the map $g \in C(Y, R)$, endowed with fine topology.