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The axiom of choice, Tychonoff's theorem, and the open mapping theorem [0, 1, 2]. Each one took me, in my view, much too long to grasp. [0] https://en.wikiped
by jethkl 4y ago
The axiom of choice, Tychonoff's theorem, and the open mapping theorem [0, 1, 2]. Each one took me, in my view, much too long to grasp.
[0] https://en.wikipedia.org/wiki/Axiom_of_choice https://en.wikipedia.org/wiki/Axiom_of_choice
[1] https://en.wikipedia.org/wiki/Tychonoff%27s_theorem https://en.wikipedia.org/wiki/Tychonoff%27s_theorem
[2] https://en.wikipedia.org/wiki/Open_mapping_theorem_(functional_analysis) https://en.wikipedia.org/wiki/Open_mapping_theorem_(function...
- kccqzy 4y agoThe axiom of choice is the topic of one whole quarter of set theory in my undergraduate years. I still don't think I fully understand it. By "fully understand it" I mean achieving the level of proficiency of my professor who, upon hearing seemingly any theorem encountered in undergraduate study, would immediately tell you whether it requires Axiom of Choice, merely Dependent Choice, Countable Choice, or doesn't require Choice.