In set theory, the properties of the set are properties of the elements in the set. Conversely, the properties of the all elements in the set are properties of the set. Considering space as a set of elemental points, then each point has the properties of the set. Basic properties of points in space can be listed as flux, impulse, acceleration, velocity, distance, surface area, volume and expansion. All these properties are related to each other in the mathematical form of a Taylor series expansion.

The Taylor series is a mathematical relationship between derivatives of these properties and integrals of time. Each element of the series has two parts, a derivative of spatial property multiplied by an integral of time. Here is an example of Distance expressed as a Taylor series:

The geometric and mathematical model of local space-time can be viewed as a dot product of an array of spatial properties and a series expansion of time. Starting with the series expansion of the exponential of time:

Each element of this expansion can be placed as an element in a time array and the spatial properties can be placed as elements of an array. The dot product of these two Wronskian arrays is space-time.

This dot product forms a Taylor series where each element of the series is considered as a domain. It is the domains, Xn, viewed as separate domains that constitute the structure and the behavior of space-time as seen by mankind. The following pages depict the domains and their corresponding Taylor series for each element of the spatial point properties. Note that by bounding the distance domain, the acceleration and impulse domain appear spherical.

The Taylor Series Equations of Space-Time