ag.algebraic geometry – C-open and Zariski open

Given the following definition:

If $V$ is an algebraic scheme over $k$, a (Zariski) $c$-open subset in $V$ is the complement of the union of a countable collection of Zariski closed irreducibles subsets in $V$.

I would like to know if a $c$-open subset in $V$ is a Zariski open subset in $V$, and viciversa.

I think that any $c$-open subset in $V$ is Zariski open subset in $V$, but maybe I am wrong. Also if you could give me any references about $c$-open subsets I will be very grateful.