Lakes of Wada
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In mathematics, the lakes of Wada (和田の湖 Wada no mizuumi?) are three disjoint connected open sets of the plane or open unit square with the counterintuitive property that they all have the same boundary.
Description
More than two sets with the same boundary are said to have the Wada property; examples include Wada basins in dynamical systems.
The lakes of Wada were introduced by Kunizō Yoneyama (1917), who credited the discovery to Takeo Wada.
His construction is similar to the construction by Brouwer (1910) of an indecomposable continuum, and in fact it is possible for the common boundary of the three sets to be an indecomposable continuum.
See also
External links
- Lakes of Wada @ Wikipedia
