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## Homework Statement

I want to show that if [tex]C[/tex] and [tex]D[/tex] and closed sets, then [tex]C \bigcup D[/tex] is a closed set.

## Homework Equations

A set is called closed iff the set contains all of its accumulation points.

## The Attempt at a Solution

In order for me to prove this statement, I will be able to use the fact that [tex]C[/tex] and [tex]D[/tex] are closed sets. Can I prove this statement by supposing that if [tex]c[/tex] is an accumulation point of [tex]C[/tex] and [tex]d[/tex] is an accumulation point of [tex]D[/tex], then both [tex]c[/tex] and [tex]d[/tex] will be accumulation points of [tex]C \bigcup D [/tex] ?