Are nite dimensional fuzzy normed spaces simpler than innite dimensional ones? These questions
are rather natural. They are important since nite dimensional spaces and subspaces play a role in various
considerations (for instance, in approximation theory). Quite a number of interesting results can be said
in this connection. Hence it is worthwhile to collect some relevant facts, for their own sake and as tools
for our further work. This is our program in this section and the next one.