Finite Union of Closed Sets is Closed

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Theorem

Topology

Let $T = \struct {S, \tau}$ be a topological space.


Then the union of finitely many closed sets of $T$ is itself closed.


Normed Vector Space

Let $M = \struct {X, \norm {\, \cdot \,} }$ be a normed vector space.


Then the union of finitely many closed sets of $M$ is itself closed.