I have been told that one can, in some sense construct line like entities, for which have more then two 'end points' such as splines/polylines and other multi-dimensional or odd entities. Although are there any other multi-dimensional kind of lines, that would allow one to speak meaningfully about their length. If so if one knows of any pictures of mathematical programs that would allow me to picture to degree such entities, I would be grateful to know.
The issue is that if one wants to model as I am attempting, a certain probability space; such that
(1) The probabilities values can be given by taking some kind of metric, or length, (rather then say a volume or areas), over a singular interval, ie max-min (or b-a) akin to a lebesque measure but
(2)such that, all of the outcomeswhen n>4 are connected are connected, so that there has to be at least three end points for n=3, four endpoints for n=5 (for each possible outcome that it connects with_.
So that
(3), As the probabilities increase and decrease they remain supersets/subsets of their original length or interval;
(B) but in such a fashion that they are still one singular continuous unbroken intervals (not sums of intervals)
(C) Can be still defined in terms of said Length if need to be (or at least given truth conditions of this form, (whilst there might be other semantics)
I can do this without this, but its somewhat ungainly
(D) When they contract and expand they expand into the territory of all of the other outcomes, not just the adjacent outcomes, or two adjacent outcomes (which works for n=3, if its contructed on a circle)
(D) and Thus such disjunctions to some degree are also continous unbroken intervals
This is an interesting question.
A step in the direction of multiple endpoints for polylines is given in
https://www.researchgate.net/publication/222041389_A_spatial_model_for_complex_objects_with_a_broad_boundary_supporting_queries_on_uncertain_data
More to the point, an intensive study of polylines is given in
https://arxiv.org/pdf/1604.07476.pdf
Article A spatial model for complex objects with a broad boundary su...
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