Timeline for Short exact sequences every mathematician should know

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Jun 21, 2020 at 20:04	comment	added	Terry Tao		Evaluating at a single element of $\beta {\mathbb N}/{\mathbb N}$ one obtains the short exact sequence $0 \to o({\mathbb R}) \to O({\mathbb R}) \to {\mathbb R} \to 0$, where $O({\mathbb R})$ is the ring of bounded nonstandard reals, $o({\mathbb R})$ is the ideal of infinitesimal nonstandard reals, and ${\mathbb R}$ is the standard reals. Also can't resist mentioning the variant $0 \to o({\mathbb Q}) \to O({\mathbb Q}) \to {\mathbb R} \to 0$, which one way to construct the real numbers in nonstandard analysis. More generally one has the nonstandard hull construction in metric or Banach spaces.
Jun 21, 2020 at 18:11	history	edited	Tomasz Kania	CC BY-SA 4.0	added 139 characters in body
Jun 21, 2020 at 18:05	history	made wiki			Post Made Community Wiki by S. Carnahan♦
Jun 21, 2020 at 17:52	comment	added	Nik Weaver		The "commutative analog" of my example! Might be worth mentioning that $l_\infty/c_0$ is isomorphic to $C(\beta\mathbb{N}\setminus \mathbb{N})$.
Jun 21, 2020 at 17:39	history	answered	Tomasz Kania	CC BY-SA 4.0