Space

Mammal is a subset of Animal.

It seems reasonable that Vector Space should be a subset of Space.

One reference mentions that we have several types of numbers but there is no general notion for a number and therefore “number” is like “space”.

Results of Our Project

We are working with several ideas:

• Vector Space is a subset of Set.
• Space needs to be more general than Vector space but more specific than set.
• Vector Space needs to have “cousins”.

A space is a Set with some Structure. Structure is the result of imposing rules which must be true.

This explanation is very similar to what was found on Wikipedia at the time of the project.

Appendix D

We have created an allegory where the collection of roads is the structure.

If you can only drive your car on roads, then the roads determine where you can drive.

One person says, the roads create the rules.

Another person says, the roads are there because of the rules.

Perhaps our best answer is to say there is a correlation, an interplay, between the roads and the rules.

Vector S