Nov 5, 2012
Topology: Connected components, etc.
I'm going to have to look up Munkres' Topology again for explicit and thoroughly elaborated proofs and explanations on connected spaces, connected components, and I'll have to take a look again at it to distinguish and clarify what the differences are between connected components, locally connected, path-connectedness, locally path-connected, arcwise-connected, and locally arcwise-connected. Whew.
Bredon's Geometry and Topology is a pain here as it is terse on explanations.
Note that these comments are all coming from a physicist.