0
$\begingroup$

A hierarchy $H$ on $E$ is defined by 3 properties:

  1. $E$ belongs to $H$
  2. if $X$ and $Y$ both belong to $H$ then either they are disjoint or one is included in the other one (i.e. their intersection equals the empty space, $X$ or $Y$).
  3. if $s$ belongs to $E$, then the singleton $\{s\}$ belongs to $H$

How would one call a structure that matches the first two properties but not the third (i.e. some singletons may be missing)?

Also, a dendrogram does not seem to correspond well to such a structure because the union of all leaves would not equal to whole set $E$. What representation should I use?

  • 1
    Were the tags chosen by rolling a D12 die? – 2017-01-13
  • 0
    Why? This doesn't help... Please do you have an answer? – 2017-01-17
  • 0
    The question is, why do you want to talk about structures that satisfy this property? Would you care to construct one? – 2017-06-15
  • 0
    How you represent this structure will probably depend on what you're using it for. – 2017-06-15
  • 0
    An example of such structure: family of ultrametric balls in ultrametric space. – 2017-06-15

0 Answers 0