In
mathematics, a
pathological phenomenon is one whose properties are considered atypically bad or
counterintuitive; the opposite is
well-behaved. A notable case is the
Alexander horned sphere, a counterexample showing that topologically embedding the sphere
S2 in
R3 may fail to "separate the space cleanly", unless an extra condition of
tameness is used to suppress possible
wild behaviour. See
Jordan-Schönflies theorem.