Σ-compact space

A topological space is called compact - countable at infinity or if it can be written as a countable union of compact subspaces. - Compactness is thus a weakening of the topological notion of compactness. The letter in the name is because the union of sets used to be referred to as sum, the name was formed the same way as " finite ".

The term is important for the abstract theory of integration, together with local compactness and the separation axiom T3, it guarantees the existence of a compact exhaustion.

For example, is equipped with the standard topology, and a - compact topological space, because it is so that this can be represented as a countable union of compact topological spaces.

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