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Self-unlinked Simple Closed Curves
| Content Provider | Semantic Scholar |
|---|---|
| Author | Henderson, David B. |
| Copyright Year | 1965 |
| Abstract | interiors of a collection of disjoint 3-cells each of diameter less than S. A set X is locally tame at p if p has a closed neighborhood in X which is a tame complex in M. If X is not locally tame at p then p is a wild point of X. A set is called nicely wild if the union of its wild points is a tame 0-dimensional set. For J an arc or scc we make the following definitions, the first of which is used in [1]. The penetration index P(J,x) of J at a point x E J is the smallest cardinal number n such that there are arbitrarily small 2-spheres enclosing x and containing no more than n points of J. The penetration index P(J) of J is the least upper bound of the cardinal numbers P(J, x), for all x E J. If J is nicely wild, then the nice penetration index NP(J) of J is the smallest integer n such that, for every E > 0, the set of wild points of J can be covered by the interiors of a collection of disjoint 3-cells each with diameter less than s and such that the boundary of each 3-cell intersects J in no more than n points. (The union of members of this collection is called a taming s-set of J of index n.) CONJECTURE. There is a nicely wild scc J such that NP(J) # P(J). |
| Starting Page | 470 |
| Ending Page | 480 |
| Page Count | 11 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9947-1965-0187234-2 |
| Volume Number | 120 |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/1965-120-03/S0002-9947-1965-0187234-2/S0002-9947-1965-0187234-2.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9947-1965-0187234-2 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
