Exhaustion by compact sets
0In mathematics, especially general topology and analysis, an exhaustion by compact sets of a topological space X is a nested sequence of compact subsets K_(i) of X (i.e. K₁ ⊆ K₂ ⊆ K₃ ⊆ ⋯), such that K_(i) is contained in the interior of K_(i + 1), that is K_(i) ⊆ int(K_(i + 1)) for each i and $X=\bigcup_{i=1}^\infty K_i$. A space admitting an exhaustion by compact sets is called exhaustible by compact sets.
For example, consider X = ℝ^(n) and the sequence of closed balls K_(i) = {x : |x| ≤ i}.
Occasionally some authors drop the requirement that K_(i) is in the interior of K_(i + 1), but then the property becomes the same as the space being σ-compact, namely a countable union of compact subsets.
Source: https://en.wikipedia.org/wiki/Exhaustion_by_compact_sets
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