Are nite dimensional fuzzy normed spaces simpler than in nite 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.
