ChapterZero

I’ve gotten myself to do some more reading of the real analysis book, and I’m now on the part about properties of topological spaces. Like Hausdorff spaces, normal, and regular spaces. All of the various properties get foggy in my mind, except for the Hausdorff; that one I see some point in. In order to test my understanding of the concepts involved, I am trying to see why, if not come up with a proof of why, it is true that a compact set in a Hausdorff space is closed.

Baby steps, I know, but I need to know all this stuff before I dive into more interesting waters. It always amazes me to see how the plethora of definitions at the beginning of any math book usually resolve themselves into practical (albeit abstract uses by its end.

Possibly relevant posts:

• Hilbert space class (7/7/2005)
• Definitions (5/9/2005)
• Topology (4/28/2005)