CounterExampleWiki:About

From CounterExampleWiki

This wiki is intended to be a repository of mathematical counterexamples. The idea is to provide a reference to help with answering questions like "Are all locally connected spaces connected?" or "Does existence of a power series imply analyticity?" More generally, this wiki is 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?