Everything about Isolated Point totally explained
In
topology, a branch of
mathematics, a point
x of a
set S is called an
isolated point,if there exists a
neighborhood of
x not containing other points of
S.
In particular, in a
Euclidean space (or in a
metric space),
x is an isolated point of
S, if one can find an
open ball around
x which contains no other points of
S.
Equivalently, a point
x isn't isolated if and only if
x is an
accumulation point.
A set which is made up only of isolated points is called a
discrete set. A discrete subset of Euclidean space is
countable; however, a set can be countable but not discrete, for example the rational numbers. See also
discrete space.
A closed set with no isolated point is called a
perfect set.
The number of isolated points is a
topological invariant, for example if two
topological spaces and
are
homeomorphic, the number of isolated points in each is equal.
Examples
Topological spaces in the following examples are considered as
subspaces of the
real line.
Further Information
Get more info on 'Isolated Point'.
|
External Link Exchanges
Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:
<a href="http://isolated_point.totallyexplained.com">Isolated point Totally Explained</a>
Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned. |
