Fuzzy hyperconnected proximity spaces and fuzzy summability over CW complexes. Application of Smirnov fuzzy similarity in video analysis

Abstract

This article introduces proximal cell complexes in a hyperconnected space. Hyperconnectedness encodes how collections of path-connected sub-complexes in a Alexandroff-Hopf-Whitehead CW space are near to or far from each other. Several main results are given, namely a hyperconnectedness form of CW (Closure Finite Weak topology) complex, the existence of continuous functions that are paths in hyperconnected relator spaces and hyperconnected chains with overlapping interiors that are path graphs in a relator space. The centroids of surface holes in an image are used as seed points for the triangulation. An application of these results to the definition of cycles using the centroids of triangles is given.