Analysis situs or topology as a new branch of mathematics emerged in the 19th century from a handful of advancements in the study of geometry, notably projective geometry, non-Euclidean geometries (spherical, elliptical, and hyperbolic), differential geometry, and graphs theory. Today, it is broken down into two somewhat disjointed subdivisions. (1) Point set topology studies geometric shapes as collections of points and calling each whole collection as a mathematical space (e.g. metric spaces, tangent spaces, fiber bundles, manifolds, etc.). On the other hand, (2) combinatorial or algebraic topology considers geometric shapes as aggregates of smaller building blocks, analogous to a solid wall is a collection of bricks (e.g. theories of atoms, molecules, planets, stars, and galaxies). The first could well be used to describe the mathematical structures of the space-time continuum (e.g. differential geometry of general relativity). The second could well be used to describe the mathematical structure of the space-time quantization (e.g. all sorts of quantum theories).

However, a complete theory of quantized space-time would necessarily incorporate both topologies and the main task is to find a mathematical or physical connection between them. Fortunately, this physical connection is the concept of energy as defined in physics. Using a deductive approach, general to specific, top down one-to-many correspondence, the space-time continuum (S) is the product of energy and vacuum lightspeed: S=cE while the quantum of space-time (H) is equivalent to the square of energy: H=E. These are used to formulate a new definition of linear momentum (p) as the ratio of H over S: p=H/S. This is simplified into E/cE or E/c. Consequently, p=E/c specifies exactly the linear momentum of light as the source of the electromagnetic field of the vacuum allowing light to move at a constant speed which implies the direct variation between energy and linear momentum such that vacuum lightspeed remains constant within the space-time continuum wherever and whenever there is a dimensional dynamic equilibrium between the twelve edges of space-time cubic lattices of space-time charges: H-plus and H-minus.