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As a counter example, it motivated the extra condition of tameness which suppresses the kind of wild behaviour the horned sphere exhibits.Like many other pathologies, the horned sphere in a sense plays on infinitely fine, recursively generated structure, which in the limit violates ordinary intuition. In this case the topology of an ever descending chain of interlocking loops of continuous pieces of the sphere in the limit fully reflects that of the common sphere, and we'd expect the outside of it, after an embedding, to work the same. Yet it does not: it fails to be simply connected.For the underlying theory, see Jordan Schnflies theorem.This article does not cite any sources.

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