  In this short note, we give a characterization of Fr\'{e}chet spaces via
properties of their metric. This allows us to prove that the Hausdorff measure
of noncompactness (MNC), defined over Fr\'{e}chet spaces, is indeed an MNC. As
first applications, we lift well-known fixed-point theorems for contractive and
condensing operators to the setting of Fr\'{e}chet spaces.
