filter notation

Question

I've come across this notation

$$\cal D^+,$$

where $\cal D$ is a filter over some cardinal $\lambda.$ If I remember correctly they said that this is the set of all positive sets, but I cannot remember precisely what was the definition of $\cal D^+$.

Answer 1

A set $A \subseteq \lambda$ is $\mathcal{D}$-positive if for every $B \in \mathcal{D}$, $A \cap B \neq \emptyset$.