Difference between revisions of "Connection number"
From Encyclopedia of Mathematics
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| − | The cardinality of the family of connectivity components in a topological space. For example, if from the real line one removes < | + | {{TEX|done}} |
| + | The cardinality of the family of connectivity components in a topological space. For example, if from the real line one removes $n$ points $a_1<\ldots<a_n$, then the components of the remainder are the sets | ||
| − | + | $$(-\infty,a_1),(a_1,a_2),\ldots,(a_n,\infty),$$ | |
| − | and so the connection number is | + | and so the connection number is $n+1$. |
| − | The term "connection number" is also used in the following sense. A domain in a Euclidean space is called | + | The term "connection number" is also used in the following sense. A domain in a Euclidean space is called $n$-connected if its boundary consists of $n$ disjoint connected subsets. For example, the interior of a disc is a $1$-connected domain, the interior of an annulus is $2$-connected. |
Revision as of 14:51, 19 April 2014
The cardinality of the family of connectivity components in a topological space. For example, if from the real line one removes $n$ points $a_1<\ldots<a_n$, then the components of the remainder are the sets
$$(-\infty,a_1),(a_1,a_2),\ldots,(a_n,\infty),$$
and so the connection number is $n+1$.
The term "connection number" is also used in the following sense. A domain in a Euclidean space is called $n$-connected if its boundary consists of $n$ disjoint connected subsets. For example, the interior of a disc is a $1$-connected domain, the interior of an annulus is $2$-connected.
How to Cite This Entry:
Connection number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Connection_number&oldid=31869
Connection number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Connection_number&oldid=31869
This article was adapted from an original article by V.I. Malykhin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article