Isolated Point

Also found in: Wikipedia.

isolated point

[′ī·sə‚lād·əd ′point]
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 ?
is semi discrete, if and only if it has a semi isolated point.
The digitally literate clients of today now effortlessly utilise the best sources of online intelligence to track agencies and work on a daily basis - not simply at the isolated point of searching for a new partner.
n])) is infinite, then no isolated point of [omega](x, ([f.
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.
We want someone capable of seeing a big, complicated, important relationship that will affect American interests for decades to come--not someone who seizes on one isolated point or sticks to a slogan.
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.
We now introduce the notions of interior and isolated point, in a general form adapted to our framework.
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.
In particular, T has SVEP at every isolated point of [sigma](T).

Full browser ?