Timeline for Is the homeomorphism class of a connected open set of C determined by its fundamental group?
Current License: CC BY-SA 3.0
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| when toggle format | what | by | license | comment | |
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| Jun 2, 2013 at 18:33 | vote | accept | Hugo Chapdelaine | ||
| May 31, 2013 at 21:13 | comment | added | Paul Fabel | To fill in a few details in the above, suppose K and K' are nonempty compact totally disconnected subsets of the 2-sphere, with respective complements U and U'. Then any homeomorphism between U and U' extends to a homeomorphism of the 2-sphere, and any homeomorphism between K and K' extends to a homeomorphism of the 2-sphere. For the latter direction, see the pf. in Van Mill's book on infinitely dimensional topology that the Cantor set cannot be wildly embedded in the plane. For the former direction apply the Schoenflies theorem repeatedly. | |
| May 31, 2013 at 20:44 | history | answered | Paul Fabel | CC BY-SA 3.0 |