  Let $T:E\rightarrow F$ be a non-necessarily continuous triple homomorphism
from a (complex) JB$^*$-triple (respectively, a (real) J$^*$B-triple) to a
normed Jordan triple. The following statements hold:
  (1) $T$ has closed range whenever $T$ is continuous
  (2) $T$ has closed range whenever $T$ is continuous
  This result generalises classical theorems of I. Kaplansky and S.B. Cleveland
in the setting of C$^*$-algebras and of A. Bensebah and J.P\'erez, L. Rico and
A. Rodr'\iguez Palacios in the setting of JB$^*$-algebras.
