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In reply to "limit point", posted by Jennifer on Sept 24, 2004:
>I have a basic question. Thanks a lot.
>
>Is every point of every open set E (is contained in R^2) a limit point of E?
Yes, it is. If O is open and x is in O then some open ball B(x,e) is contained in O
(as x is an interior point of O).
But open balls in R^2 have the property that they contain many more points than just x
(eg also (x_1 + 1/2*e, x_2) for x = (x_1, x_2), and e>0 ) and so if B(x,r) is any neighbourhood
of x, then B(x, min(r,e)) will contain this point, which is in O (as B(x,e) \subset O) and not equal to x.
So x is a limit point of O.
>In case of for clsed sets in R^2?
>
There it fails, eg if C = {(1/n, 0): n in N}.
No point of C is a limit point of C (but (0,0) is), as is easily checked.
Henno
What else can I help you with?
Why singleton set is not open in Q?
In the context of the rational numbers ( \mathbb{Q} ) with the standard topology induced by the real numbers ( \mathbb{R} ), a singleton set ( {q} ) (where ( q ) is a rational number) is not open because for any point ( q ) in ( \mathbb{Q} ), every open interval around ( q ) contains both rational and irrational numbers. Therefore, any interval ( (q - \epsilon, q + \epsilon) ) intersects with points outside the singleton set, meaning it cannot be entirely contained within ( {q} ). Thus, singleton sets do not satisfy the definition of an open set in ( \mathbb{Q} ).
What does open circle mean in math?
An open circle is usually found on a number line in math. An open circle usually represents a number that is not included in the line.
What does topologically equivalent mean?
Two metrics on the same set are said to be topologically equivalent of they have the same open sets. So if an open subset, U contained in M is open with respect to one metric if and only if it is open with respect to the other metric. Another way to think of this is two objects are topologically equivalent if one object can be continuously deformed to the other. To be more precise, a homemorphism, f, between two topological spaces is a continuous bijective map with a continuos inverse. If such a map exists between two spaces, the are topologically equivalent.
When was OPEN CASCADE created?
OPEN CASCADE was created in 2000.
How do you bisect an angle?
Take a compass. Open it so that it is a large enough radius to be easy to draw, but small enough that it still marks on both lines of the angle. Draw an arc that crosses both lines making up the angle, then place the point on each of these intersections and draw two more arcs of the same size so that they intersect. Using a straightedge, draw a line from the point of the angle to the intersection. That is the bisecting line.
What is an Open and Dense set?
a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of Aan open set is an abstract concept generalizing the idea of an open interval in the real line
Is a set of isolated points a closed set?
Take the set of points 1/n for all integers n. This is an isolated set of points- that is, for any of them there is an open ball about the point not containing any other point. However, this set has a limit point which is not contained in the set (namely 0), hence it is not closed.
In calculus do open sets have accumulation points?
Yes, every point in an open set is an accumulation point.
Is a point is a zero dimensional?
In mathematics, a zero-dimensional topological space is a topological space that ... any point in the space is contained in exactly one open set of this refinement.
Why is every singleton set in a discrete metric space open?
In a metric space, a set is open if for any element of the set we can find an open ball about it that is contained in the set. Well for the singletons in the discrete space, every other element is said to have a distance away of 1. So we can make a ball about the singleton of radius 1/2 ... this ball just equals that singleton since it contains only that element. So it is contained in the set. Thus the singleton set is open.
In which class either lower limit or upper limit is missing?
open end class
What is the open set in topology?
There are actually more than a definition of the open set in topology. They are:A set containing every interior point.A set containing a point along the region such that you can form the open ball.
Who can be a member of the crips?
There is no age limit or race limit to being allowed to be a Crip and membership is open to males and females.
What is the speed limit on the open road at daytime?
45 mpk
What are the parts of open office org?
The programs contained within Open Office are:- Base, Calc, Draw, Impress, Math & Writer
What does junior open level 3 mean in cheerleading?
A junior team can not be Open. Only senior teams can be open. Open means there is no age limit.
How do you open time limit on black ops?
you will have to go to team deathmatch and open up the options, it will show a time limit and the number of opponents you want against and some other crap.
