Empty space connected? If so, then what are its components? I encountered that a topological space $X$ is connected if no separation exists. Here
a separation is a pair of disjoint non-empty open sets whose union
is $X$. Such a separation can only exist if $X$ contains two distinct
elements, so $\emptyset$ is supposed to be connected (right?). But
what about its components? Does it have $\emptyset$ as unique component
or are there in this case no components at all? They should form a
partition of $\emptyset$, and I was taught that elements of a partition
are non-empty.

The set of components is $\emptyset$, i.e., there are no components. The statement "every component is non-empty" is then trivally true.
