[I'm tired, I should be writing this for the nonsense but I can't be bothered schleping HTML tonight. So you're stuck with my tripe here. It will be nonsense to most. Perhaps to all?]
The toplogy TMA will not be finished; one and a half units/questions undone, and the thing to be posted by 17:30 Thursday—not going to happen.
Tonight I managed thirteen of the hardest marks that I may never get. Still I had a light-bulb moment. [This is a live TMA so I'm going to obfuscate this.]
For some reason I thought that I could manage a proof-by-contradiction (sometimes I can) after a while I realized that, while I was right, [I knew that from the way the question was worded] this wasn't going to work out. Where to now?
That's the problem with topology—the tool kit is too big. And you don't know what some of the tools are really for. And you often pick the wrong tool.
For example, tonight I needed to show that some set in some space was bounded, that would be the General Extreme Value theorem then? No! that says that something entirely different. So ... what? Monotone convergenge, that isn't even listed in the hand book ... do I really need to show that this is bounded?
People who know this stuff will guess the method that I used. Weierstrass and his ilk may have been the rightest of the right but they have blown the brains of generations of undergrads. Maybe that's our due?
When this course finishes I won't be walking away from topology. This course has been too-far too-fast but I've always seen maths as a girl...a girl like me, a girl who likes me.
And...