In the real setting, the Banach-Stone theorem says that given two
compact spaces
X and
Y, the existence of an isometry between
C(
X) and
C(
Y) (endowed with the sup norm) implies that
X and
Y
are homeomorphic. It is also known that, in the same context, a
similar result can be obtained if there exists a linear isomorphism
satisfying
.
Here we deal with isomorphims between spaces of p-adic valued
functions endowed with an A-norm, and study when a homeomorphism
between topological spaces can be obtained.