finite intersection property
The finite intersection property is most often used to give the following http://planetmath.org/node/3769equivalent condition for the http://planetmath.org/node/503compactness of a topological space (a proof of which may be found http://planetmath.org/node/4181here):
An important special case of the preceding is that in which is a countable collection of non-empty nested sets, i.e., when we have
In this case, automatically has the finite intersection property, and if each is a closed subset of a compact topological space, then, by the proposition, .
- 1 J. Munkres, Topology, 2nd ed. Prentice Hall, 1975.
|Title||finite intersection property|
|Date of creation||2013-03-22 13:34:05|
|Last modified on||2013-03-22 13:34:05|
|Last modified by||azdbacks4234 (14155)|
|Synonym||finite intersection condition|
|Defines||finite intersection property|