(a) The curves z(s) and z(s, t) were not required to be simple curves. This made the task of approximating them with continuously differentiable curves very easy. (b) The Cauchy integral theorem also holds if the function z(s) describing the curve C is merely piecewise continuously differentiable. For in this case we carry out the integration by parts in (6) over each subinterval on which zs(s)...

The aim of this paper is to continue the research work that we have done in a previous paper published in this journal see Mihail andMiculescu, 2008 . We introduce the notion of GIFS, which is a family of functions f1, . . . , fn : X → X, where X, d is a complete metric space in the above mentioned paper the case when X, d is a compact metric space was studied andm,n ∈ N. In case that the funct...

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat’s principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a class...