|
|
|
|
exhaustion by compact sets
|
(Theorem)
|
|
|
Let $U$ be an open set in
 (or a manifold with countable base). Then there exists a sequence of compact sets $K_1, K_2, \ldots$ such that \begin{eqnarray*} K_i &\subseteq& \operatorname{int} K_{i+1}, \quad i=1,2,\ldots, \\ U &=& \cup_{i=1}^\infty K_i, \end{eqnarray*}where ``$\operatorname{int}$ '' denotes the topological interior. Such a sequence is called an exhaustion by compact sets for $U$ .
|
"exhaustion by compact sets" is owned by matte. [ full author list (2) ]
|
|
(view preamble | get metadata)
Cross-references: interior, compact sets, sequence, base, countable, manifold, open set
This is version 3 of exhaustion by compact sets, born on 2005-05-22, modified 2005-05-22.
Object id is 7103, canonical name is ExhaustionByCompactSets.
Accessed 1780 times total.
Classification:
| AMS MSC: | 53-00 (Differential geometry :: General reference works ) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
