Is $D=\{z:|z-z_0|\le r\}$ an open or closed set?

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My doubt arises from the Wikipedia page on the Cauchy integral formula, where the set $D=\{z:|z-z_0|\le r\}$ is defined as an open set.

As it includes also its boundary points $|z-z_0|=r$, shouldn't it be defined a closed set? (while $D=\{z:|z-z_0|\lt r\}$ be an open set?)

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José Carlos Santos made a comment instead of an answer, otherwise I would have flagged his response as correct. Indeed, D is never referred as a open set, but as a closed disk contained in the U open subset of the complex plane. My mistake.