Space

We don’t have a definition for space that is more General than Vector space. If you go on the internet to find articles about space, almost every page you find will be about vector spaces.

Appendix A

Hypothesus: A space isn’t useful until it has all the features we need such as things like being able to measure distance between two points, and the distances between adjacent integers to be equal. By the time a space has all the features we need, it’s a vector space.

Appendix B

We all love Star Trek and when we hear the word space we think of a structure that is three-dimensional.

However, it is helpful to us to say we’re going to generalize this so that it can include plane segments and line segments. Sometimes when you are learning something new, it helps to only have to consider one dimension.

Appendix C

We found this sentence

“A scalar field assignments a scalar to every point in a space.”

We believe a space starts out as a collection of points.