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Tomas Paul
Tomas Paul
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Call a "blot" set, which is the closure of its interior, the boundary is locally connected, and when you remove boundary blot remains connected. Suppose that there is a blot on the surface of the n-dimensional sphere. Is it true that every homeomorphism of the blots on itself extends to a homeomorphism of the sphere on itself? If this is not true, can it be imposed on the blot any additional reasonable conditions (eg, local connectedness of the boundarysmoothness) to the statement was true?

Call a "blot" set, which is the closure of its interior, connected, and when you remove boundary remains connected. Suppose that there is a blot on the surface of the n-dimensional sphere. Is it true that every homeomorphism of the blots on itself extends to a homeomorphism of the sphere on itself? If this is not true, can it be imposed on the blot any additional reasonable conditions (eg, local connectedness of the boundary) to the statement was true?

Call a "blot" set, which is the closure of its interior, the boundary is locally connected, and when you remove boundary blot remains connected. Suppose that there is a blot on the surface of the n-dimensional sphere. Is it true that every homeomorphism of the blots on itself extends to a homeomorphism of the sphere on itself? If this is not true, can it be imposed on the blot any additional reasonable conditions (eg, smoothness) to the statement was true?

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Tomas Paul
Tomas Paul
  • 181
  • 1
  • 4

Extension of homeomorphisms on a spherical space

Call a "blot" set, which is the closure of its interior, connected, and when you remove boundary remains connected. Suppose that there is a blot on the surface of the n-dimensional sphere. Is it true that every homeomorphism of the blots on itself extends to a homeomorphism of the sphere on itself? If this is not true, can it be imposed on the blot any additional reasonable conditions (eg, local connectedness of the boundary) to the statement was true?