Closed Loop Interval Ontology
     CLOSED LOOP INTERVAL ONTOLOGY
       The Digital Integration of Conceptual Form

ORIGIN

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Compactification
Preserving data under transformation

We are saying that the closed loop can compress the structure of hierarchy into a single form -- maybe a single interval, maybe a single line, maybe a single point

Compactification is a known subject. The "point at infinity" is a very appropriate symbol of why this is interesting.

Compactification
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make a topological space into a compact space

We are interested in this theme because we exploring the claim that a vastly complex hierarchical structure containing a huge amount of data can be compactified into a straight line or continuum -- possibly of zero thickness

Sat, Apr 17, 2021

Reference
In mathematics, in general topology, compactification is the process or result of making a topological space into a compact space. A compact space is a space in which every open cover of the space contains a finite subcover. The methods of compactification are various, but each is a way of controlling points from "going off to infinity" by in some way adding "points at infinity" or preventing such an "escape".

URL
https://en.wikipedia.org/wiki/Compactification_(mathematics)

Point at infinity
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In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.

In the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane. Adjoining these points produces a projective plane, in which no point can be distinguished, if we "forget" which points were added. This holds for a geometry over any field, and more generally over any division ring.[1]

In the real case, a point at infinity completes a line into a topologically closed curve. In higher dimensions, all the points at infinity form a projective subspace of one dimension less than that of the whole projective space to which they belong. A point at infinity can also be added to the complex line (which may be thought of as the complex plane), thereby turning it into a closed surface known as the complex projective line, CP1, also called the Riemann sphere (when complex numbers are mapped to each point).

In the case of a hyperbolic space, each line has two distinct ideal points. Here, the set of ideal points takes the form of a quadric.

Fri, Apr 2, 2021

URL
https://en.wikipedia.org/wiki/Point_at_infinity