SINGULARITIES IN QUASI-BANACH SPACES WITH APPLICATIONS TO SEMILINEAR ELLIPTIC-EQUATIONS .1.

The paper deals with the extension of the singularity theory which was elaborated for Banach spaces to quasi-Banach spaces. For general quas i-Banach spaces some striking tools fail: not locally convex, the dual space may be trivial,.... Applying the concept of dual rich quasi-Ban ach spaces and results about Fredholm maps some results of the classic al theory can be carried over. As an application we show in the contin uation of this part how one can use these results for the investigatio n of the solution structure of semilinear elliptic boundary value prob lems in function spaces of Besov-TriebeI-Lizorkin type.