  We investigate isomorphic embeddings $T: C(K)\to C(L)$ between Banach spaces
of continuous functions. We show that if such an embedding $T$ is a positive
operator then $K$ is an image of $L$ under a upper semicontinuous set-function
having finite values. Moreover we show that $K$ has a $\pi$-base of sets which
closures a continuous images of compact subspaces of $L$. Our results imply in
particular that if $C(K)$ can be positively embedded into $C(L)$ then some
topological properties of $L$, such as countable tightness of Frechetness, pass
to the space $K$. We show that some arbitrary isomorphic embeddings $C(K)\to
C(L)$ can be, in a sense, reduced to positive embeddings.
