Kerodon

Variant 3.2.4.14. In the situation of Lemma 3.2.4.13, the extension condition $(a_ n)$ also makes sense for $n=0$ and $n=1$. Here condition $(a_0)$ is equivalent to the requirement that $\pi _0(X)$ has at least one element (that is, $X$ is nonempty), and condition $(a_1)$ is equivalent to the requirement that $\pi _0(X)$ has at most one element (that is, $X$ is either empty or connected). In particular, $X$ satisfies conditions $(a_0)$ and $(a_1)$ if and only if it is connected.