Timeline for How can one construct this dendrite?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 7, 2021 at 13:12 | comment | added | Kevin Beanland | Thanks everyone. I got it. | |
| Sep 7, 2021 at 3:14 | comment | added | Bill Johnson | What Alessandro said. | |
| Sep 6, 2021 at 20:24 | comment | added | Alessandro Codenotti | See also the second answer here mathoverflow.net/questions/188707/… | |
| Sep 6, 2021 at 20:22 | comment | added | Alessandro Codenotti | @Kevin at each stage you make the middle point of any pair of cut point a cut point, but whenever you add a new cut point you increase the degree by 1 by adding more new segments. This is all well defined because at every stage you are adding finitely many things. (If you don't want to have to worry about constructing this as a planar continuum which requires some care in making the segments shorter and shorter just build it as a subdendrite of Wazewski universal dendrite $D_\infty$) | |
| Sep 6, 2021 at 18:54 | comment | added | Kevin Beanland | Bill: Does your construction give three cut points of degree 4 or am I reading it wrong? We need a unique cut-point for each degree. | |
| Sep 6, 2021 at 18:06 | comment | added | Bill Johnson | Start with a closed interval of length $1$. Make the center $x$ of the interval a cut point of degree 3 by attaching an interval of length $1/3$ with end point at $x$. In each component of the three intervals you have when you remove $x$, make the center $y$ a cut point of degree $4$ by attaching two intervals of length $1/4$ with end points at $y$. Et cetera. | |
| Sep 6, 2021 at 17:05 | comment | added | Kevin Beanland | @mme. Thanks, that was my guess. | |
| Sep 6, 2021 at 16:58 | comment | added | mme | The degree of a cut-point is probably the number of components it separates the space into upon deletion. | |
| Sep 6, 2021 at 16:41 | history | edited | Kevin Beanland | CC BY-SA 4.0 |
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| Sep 6, 2021 at 14:08 | history | asked | Kevin Beanland | CC BY-SA 4.0 |