[lead: your guide to many different models for space in physics. one use: 3D world in which one could live or 4D, a set of locations or places. Mathematicians use space to mean any set; the space of all functions, nobody lives int eh space of all functions it's a mathematical abstraction.]
SPACETIMES: [solutions to Einstein;s equations that tell you a particular metric on spacetime] 3 are special because have the most symmetry: the plane the sphere and the saddle.
de Sitter Space. Positive curvature
Anti-de Sitter Space. Negative curvature
Minkowski Space. 0 curvative
Misner Space. [take minkowskli space and cut in interesting ways; cylindrical space that has closed timelike curves.]
Hilbert Space. [mathematical abstraction; wave functions live in Hilbert space not spacetime. Every WF is a single point in Hilbert space]