Timeline for Compactification of a manifold
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Aug 5, 2010 at 10:28 | comment | added | rpotrie | You are right. This answer gets my vote. I was thinking that possibly it could be saved by asking to compactify with a set with empty interior (this can be done for open subsets of the plane), but the surface of infinite genus also gives a counter example of the more general statement. | |
| Aug 5, 2010 at 10:19 | comment | added | Charles Matthews | Yes, but the point made in the comments about infinitely-generated homology is already in the second sentence, really. The complement o the points (n,0) where n is an integer $can$ be compactified by adding one point for each n, then compactified in the 2-sphere. Do yo want that? | |
| Aug 5, 2010 at 10:00 | comment | added | rpotrie | If I understand the question well, the annulus you can compactify it with two points to get the sphere. The annulus is diffeomorphic to the sphere minus two points, so, it embeds there. In the remark I made, there is an example where you need to include cells, but again they are of smaller dimension. | |
| Aug 5, 2010 at 9:56 | history | answered | Charles Matthews | CC BY-SA 2.5 |