Lakes of Wada
This article describes a standard counterexample to some plausible but false implications. In other words, it lists a pathology that may be useful to keep in mind to avoid pitfalls in proofs
View other standard counterexamples in topology
Lakes of Wada is used to refer to a certain compact connected subset of whose complement has three connected components (all being open subsets). The three open sets here are the lakes. This example is closely related to the Jordan curve theorem.
References
- A First Course in Algebraic Topology by C Kosniowski, Cambridge University Press, Cambridge, 1980