Isolated Point


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isolated point

[′ī·sə‚lād·əd ′point]
(mathematics)
A point p in a topological space is an isolated point of a set if p is in the set and there is a neighborhood of p which contains no other points of the set.
A point that satisfies the equation for a plane curve C but has a neighborhood that includes no other point of C. Also known as acnode; hermit point.

Isolated Point

 

a point belonging to some set M in whose neighborhood there is no other point of the set. The points of the set M that do not satisfy this condition are its limit points. The definition of an isolated point given above presupposes that in set Mthe concept of proximity among its elements (points) has been introduced. Because of this, the concept of isolated point is topological. In particular, if M is a set of points on a straight line, then point x of this set is an isolated point if there exists an interval that contains this point and does not contain other points of set M. Thus, if M consists of points having coordinates 1, 1/2, 1/3, …, l/n, …, then each point of this set is an isolated point, but for a set consisting of the same points and of a point having the coordinate 0, the latter will not be an isolated point. The isolated points of a curve or surface (here M is the set of all points of the given curve or surface) are also considered in geometry; for example, the point (0, 0) is an isolated point of the curve y2 = x4 − 4 x2. In the theory of functions of a complex variable we speak of the isolated singular points of an analytic function; the pole of a single-valued analytic function may serve as an example of this.

References in periodicals archive ?
An operator T is said to be isoloid if every isolated point of [sigma](T) is an eigenvalue of T.
In one of the worst cases of river pollution, the sugar giant is discharging its effluents through a drain that opens into the mainstream river at an isolated point at Puth village, about 30 km from Garhmukteswar ( Brijghat) in the Ghaziabad district.
Still, the book's authors find lots to criticize, including Shanghai's "decision to accommodate growth by building high, with isolated point blocks surrounded by car ramps and empty open space, damaging the subtle urban grain of a city of immense character and dynamic street life.
Keywords: Intuitionistic fuzzy metric space, adherent point, accumulation point, isolated point, Heine theorem.
The evaluation of the six-DOF sensor accuracy for isolated point is processed in following steps:
1 (Table 2), also confirm that a "clear" TOFD scan is free of fusion defects and that isolated point reflectors are not critical enough to induce weld zone failure during bend tests.
Many customers have deployed TrackVia as their internal application platform, allowing their IT departments to consolidate, secure and integrate all their department applications in one place, while cutting software costs by as much as 80 percent over isolated point solutions.
While there is some value in exchanging information through isolated point solutions, there is far greater value in integrating all of the information into a data warehouse supported by a cross-industry data model.
Healthcare organizations and clinician users were then left to integrate isolated point technologies within their workflow and facility constraints.
Likewise, employees can no longer be seen as isolated points on a hierarchical org chart, but rather nodes in a web of networks sprawled across the organization, and beyond.
The search for flight MH370 is taking place over one of the most harsh and isolated points on the planet, in a patch of southern Indian Ocean from where Antarctica beckons.
While a massive multinational search operation for the suspicious debris of MH370 resumes in the Southern Indian Ocean, the fact that the search is taking place over one of the harshest and isolated points on the planet, is raising fear and panic.

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