Exhaustion by compact sets

In mathematics, especially analysis, exhaustion by compact sets of an open set E in the Euclidean space Rⁿ (or a manifold with countable base) is an increasing sequence of compact sets ${\displaystyle K_{j}}$, where by increasing we mean ${\displaystyle K_{j}}$ is a subset of ${\displaystyle K_{j+1}}$, with the limit (union) of the sequence being E.

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