Exhaustion by compact sets

In mathematics, especially general topology and analysis, an exhaustion by compact sets of a topological space X {\displaystyle X} is a nested sequence of compact subsets K i {\displaystyle K_{i}} of X {\displaystyle X} (i.e. K 1 ⊆ K 2 ⊆ K 3 ⊆ ⋯ {\displaystyle K_{1}\subseteq K_{2}\subseteq K_{3}\subseteq \cdots } ), such that each K i {\displaystyle K_{i}} is contained in the interior of K i + 1 {\displaystyle K_{i+1}} , i.e.

Source: Wikipedia — Exhaustion by compact sets (CC BY-SA 4.0)

Exhaustion by compact sets

In mathematics, especially general topology and analysis, an exhaustion by compact sets of a topological space X {\displaystyle X} is a nested sequence of compact subsets K i {\displaystyle K_{i}} of X {\displaystyle X} (i.e. K 1 ⊆ K 2 ⊆ K 3 ⊆ ⋯ {\displaystyle K_{1}\subseteq K_{2}\subseteq K_{3}\subseteq \cdots } ), such that each K i {\displaystyle K_{i}} is contained in the interior of K i + 1 {\displaystyle K_{i+1}} , i.e.

This neuron ends here.

Source: Wikipedia "Exhaustion by compact sets" · CC BY-SA 4.0

Share this article: X · Bluesky
Privacy Policy