Generalized cell structures (Q2673846)

In this paper, the authors present the structure of spaces as approximations of simpler and more understandable structures such as graphs. Cell structures are introduced for the study of some classes of topological spaces and their continuous functions through discrete approximations. The authors consider a weaker version of cell structures (generalised cell structures or g-cell structures). First, the authors introduce the necessary, fundamental definitions, the concept of generalised cell structure and demonstrate several basic results. Next, they prove that there are topological spaces admitting a g-cell structure but not a cell structure. The authors present a concrete example of a non-regular space with a g-cell structure.