In the area of topological space theory in mathematics, an indiscrete space is a topological space in which all the points of the space are intuitively “closely packed together” and no point is distinguishable in a topological sense. The topology of a close space is a trivial topology whose open set system consists only of the empty set and the entire space, and is often referred to as an indiscrete topology. We can think of an adjacency space as a pseudo-distance space with respect to a distance function such that the distance between any two points is zero. Close space - Wikipedia
In a system that organizes pages by tagging, “pages with a certain tag” are a subset of the entire set of pages, and in simple terms, pages that are in the set are close to each other and pages that are not in the set are far away from each other.
- This naive “near/far” is mathematically neatly defined in topology.
- The naive inclination is to say “distance,” but the mathematical requirements for distance are much stricter.
A close phase is one of the “self-evident phases (= phases that meet the definition of a phase but are not useful at all)” and is “I put the same tag on all the pages. The other obvious phase, the discrete phase, is the state in which “no page has a link” in Scrapbox. In a system where pages and tags are separate, it would be “every page has an individual tag.
Definition of a phase space by an open set system, expressed in a naive way: “If the AND and OR of a tag is also considered a tag, then the set of pages is a phase space by that tag”.
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