I'm learning real analysis.
A subset $G$ of $X$ is called open if for each $x \in G$ there is a neighborhood of $x$ that is contained in G
My question is that is $\emptyset$ a open set in $X$?
The set $\emptyset$ has no elements, so there is no neighborhood of $x$ is contained in $G$. Hence, it is not open set. However my intuitive tell me it should be a open set. What's wrong? Could anyone explain it? Thanks.