Sard and Bertini type theorems for complex spaces

Abstract

We prove that if X is a normal [reap. reduced, maximal] complex space and f: X→C is a holomorphic function, then f−1(c) is normal [resp. reduced, maximal] for all but countably many ceC. This Sard type theorem, together with a Bănică's result on the fibers of a flat map, allows us to prove Bertini type theorems for reduced and normal complex spaces.