exhaustion by compact sets

Let U be an open set in n (or a manifold with countable base).  Then there exists a sequence of compact sets K1,K2, such that

Ki intKi+1,i=1,2,,
U = i=1Ki,

where “int” denotes the topological interior.   Such a sequence is called an exhaustion by compact sets for U.

Title exhaustion by compact sets
Canonical name ExhaustionByCompactSets
Date of creation 2013-03-22 15:18:13
Last modified on 2013-03-22 15:18:13
Owner matte (1858)
Last modified by matte (1858)
Numerical id 6
Author matte (1858)
Entry type Theorem
Classification msc 53-00
Related topic MethodOfExhaustion