Everything about Hedgehog Space totally explained
In
mathematics, a
hedgehog space is a
topological space, consisting of a set of spines joined at a point.
For any
cardinal number , the
-hedgehog space is formed by taking the
disjoint union of
real
unit intervals identified at the origin. Each unit interval is referred to as one of the hedgehog's
spines. A
-hedgehog space is sometimes called a
hedgehog space of spininess .
The hedgehog space is a
metric space, when endowed with the
hedgehog metric if
and
lie in the same spine, and by
if
and
lie in different spines.
The hedgehog space is an example of a
Moore space, and satisfies many strong normality and compactness properties. Hedgehog spaces are examples of
real trees.
Paris metric
The metric on the
plane in which the distance between any two points is their
Euclidean distance when the two points belong to a
ray though the origin, and is otherwise the sum of the distances of the two points from the origin, is sometimes called the
Paris metric because navigation in this metric resembles that in the radial street plan of
Paris. The Paris metric, restricted to the
unit disk, is a hedgehog space where
K is the
cardinality of the continuum.
Kowalsky's theorem
Kowalsky's theorem states that any metric space of
weight can be represented as a subspace of the product of countably many
-hedgehog spaces.
Further Information
Get more info on 'Hedgehog Space'.
|
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://hedgehog_space.totallyexplained.com">Hedgehog space 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. |
