As a science derived from geometry, topology deals with the characteristics of physical and abstract elements that do not change when they are contorted or deformed - stretched or twisted - except when they break or tear. By definition, spaces belong to a same topological class if they can be deduced from each other by continuous deformation without cutting or tearing. This means that a 2D triangle is topologically equivalent to a circle but not to the segment of a straight line. A 3D cube could be transformed into a ball but not into a ring; a ball isn't topologically equivalent to a torus, a doughnut shaped surface generated by a circle rotated about an axis. Although a sphere exists in 3D space, its surface is two-dimensional. Similarly, a hypersphere with a three-dimensional surface curves into 4-space. The hypercube is the four-dimensional analogue of an ordinary cube and just as a 3D cube may be constructed by folding six squares together, so a 4D cube may be made by folding eight cubes into each other. A hypersphere is a sphere having more than three dimensions sharing a formula with the torus shape which is also that of the vortex. This torus shape of the hypersphere that appears widely in natural phenomena as in the magnetic field or in smoke rings is currently widely assumed to be the shape of space itself.

Topology studies space considering how spatial representation can be changed through perspective and dimensional effects. A hypersphere shows an interconnectedness of things even when they appear to be separate from one another. Not only science fiction makes use of concepts of poly-dimensionality and tells about journeys through the gravitational channels of wormholes expanding the horizon beyond the boundaries of the speed of light. For all technological diagrams and technically logical structures working with dynamic complexity, the expansion of logical space into the realm of hyper-dimensionality the assumption of more than 3 dimensions is a necessity. Amongst other uses it is applied as communication structure in parallel computing, complex information management and network topology, the science of the connective structure of information channels. Limited perspective and depth perception of relational proportions also allows for special effects illusions in the social group. The dimensionality of cognitive space accumulates attributes in the hyperweb of our world of dark attractors where gravitational forces constantly change the correlation of time and space on the fairground of attractions.