I have quite unusual question. Almost everytime I am studying math, I lowkey want to "categorize" the stuff and look at it as a bigger picture.
Do you know about any resource (diagram, article, paper) that visualizes various types of spaces, what properties they have and examples of such spaces?
I mean something like
- Topological spaces - have axioms of topology, examples are X,Y,Z...
- Metric spaces - topological spaces with metric, compactness can be defined in a different way, open sets can be defined in a different way, examples are X,Y,Z...
- Euclidean spaces - ....
I am asking, because it often happens to me that I am looking at certain definition and it only applies for ceratin kind of spaces and I know I can search for all "specializations" of any definition, but I would love to see all of it together.
Thank you in advance. If my question is too ambiguous, I will try to edit.