Singular points of weakly holomorphic functions

In this paper we are interested in two kinds of singular points of weakly holomorphic functions. Points where a weakly holomorphic function is not holomorphic and points at which it just is not continuous. The latter are closely connected to points of irreducibility of the given analytic set. We investigate the structure of such points proving they form analytically constructible sets and we study the analytic cycle obtained from this result. We prove also that non-holomorphicity points of a given weakly or c-holomorphic function form an analytic subset of the singularities and give a new criterion for a weakly holomorphic function to be holomorphic.