Abstract
This chapter contains some results from the fixed point theory in topological vector spaces which are of special interest for the fixed point theory in random normed spaces. Namely, a random normed space (S, F, T) with a continuous t-norm T is a topological vector space which is not necessarily a locally convex space. It is known that a random normed space (S, F, T) is a locally convex space when T is a continuous t-norm of H-type. In the fixed point theory in a not necessarily locally convex topological vector spaces a very useful notion is that of an admissible subset which was introduced by Klee. Many important function spaces are admissible.
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