Timeline for A question about the centroids of compact subsets of Euclidean spaces
Current License: CC BY-SA 3.0
4 events
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| Aug 26, 2016 at 20:48 | comment | added | Garabed Gulbenkian | I Can slightly modify my question to remove this flaw. If K is any non-empty compact subset of E(n), I can substitute for the centroid of K, the so-called Tchebycheff center of K. This is the center of the smallest closed ball of E(n) that contains K as a subset.. Every non-empty compact subset of E(n) contains a unique Tchebycheff center. With this change, I would not be surprised if my question about continuity had a positive answer. At least I have not been able to find any counter-examples. | |
| Aug 25, 2016 at 19:41 | comment | added | Garabed Gulbenkian | Your question made me realize that there might be something wrong with my question. I am not sure that every non-empty compact subset of a Euclidean space has a centroid. Some definitions of "centroid " might not imply that it was a unique point. Where, for example, would be the centroid of an uncountable and totally disconnected compact set such as the Cantor middle third set -which has zero Lebesgue measure. A denumerably infinite compact set might pose an even worse problem. I see why you are advocating that one should only consider sets having positive measure. | |
| Aug 25, 2016 at 19:01 | vote | accept | Garabed Gulbenkian | ||
| Aug 25, 2016 at 1:41 | history | answered | Martin M. W. | CC BY-SA 3.0 |