I'd like to understand better the significance of certain properties of topological vector spaces. It would be great if someone could give me an intuitive picture for what makes them "special", and/or illustrative examples of their nature, and/or some idea of what else we can conclude about spaces with such properties, etc.
The properties in particular that I am interested in:
- locally convex tvs, i.e. one in which every point has a local base whose members are all convex
- locally compact tvs, i.e. one in which every point has a compact neighborhood
- locally bounded tvs, i.e. one in which every point has a bounded neighborhood
- tvs with Heine Borel, i.e. one in which every closed and bounded set is compact