equivalent norms

yifli

The vector space Hom(V,W) remains the same if either the domain norm or the range norm is replaced by an equivalent norm.

Does 'remain the same' here means that the bound of every mapping in Hom(V,W) is unchanged?

How come the above theorem can be considered as a corollary of the following theorem?

If U, V and W are normed linear spaces, and if T is in Hom(U,V) and S is in Hom(V,W), then ST is in Hom(U,W) and || ST || <= ||S|| ||T||

Thanks