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In topology, two surfaces are isomorphic if they can be transformed into each other by stretching and bending, but not cutting, reattaching, or passing through theirselves. All pairs of surfaces which are isotopic are also homeomorphic, but not all homeomorphic surfaces are isotopic. A loop of string and a loop of string with a knot in it are homeomorphic but not isotopic, because in order to get from one to the other the string has to pass through itself.

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