The application of the theory of homeomorphic transformations of topological manifolds and the operation of the connected sum of manifolds for a formation of a topological model of membrane transformations during the division process of cellular and subcellular compartments, has been shown. The biological cell and the subcellular structures in the form of vesicles are modelled by an arrangement of two concentric spheres corresponding to the inner and outer layer of the membrane bounding the vesicle. The analysis shows eight succeeding topological stages of membrane transformations during the division process and these stages are characterised. It is concluded that there is a vectorial translocation of lipid molecules from the inner layer of the membrane bounding the vesicle before the division process to the outer layer of the membranes after the division process and there is no lipid translocation from the outer layer to the inner layers during the division process.