Topological spaces
- Two spaces are topologically equivalent if one can be smoothly deformed into the other without cutting or gluing. This property is independent of how we parametrize the spaces.
Thoughts
Great introductory definitions and motivation given in the first section of the book Counterexamples in Topology, by Lynn Arthur Steen and J. Arthur Seebach, Jr, and in the short document Notes on Introductory Point-Set Topology by Allen Hatcher.