Cartesianization of complex forms in Saidou’ spaces

Abstract EN

In this work, we propose to define a new space that will be called locally Cartesian space (Saidou’Spaces).

It is a space defined by a new topology whose fundamental system of neighborhood are compact cartesian subsets, theses subsets were already defined during our previous work, “Geometrical introduction to Cartesian geometry in complex shapes see [15].

It will have the same properties of a Banach space.

Then, we will give the steps of a cartesianization method of complex shapes or region in this space.

The objective sought by this technique is to find a cartesian form (denoted Car(A)), that approximates any form A, see Figure1 below.

It should be noted that cartesianization will be a generalization of the polygonization whish remains the object of research for several researchers in the spaces R2 Ref [12] [13] [6].