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From CounterExampleWiki
The idea behind this wiki is to be a repository of mathematical counterexamples, much in the same spirit as several well-known books, such as Counterexamples in Topology or Counterexamples in Analysis. (Although PLEASE don't do any bulk copying of content from those books into this wiki.) The idea is to have discussions on mathematical topics and then hopefully have discussions on counterexamples regarding those topics. For example, given a theorem, with conditions A and B, what are some counterexamples where the theorem fails if you try relax either of the two conditions? Or, given a theorem where condition X implies statement Y, what are some counterexamples for why the reverse implication does not work?
Here are some initial general categories. Feel free to add your own.
There's not much here yet, but hopefully that will change soon.
Tip
There is a Sandbox in case you need to test your edits or check out some LaTeX markup.
