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Warning Let $X$ be a topological space. If the simplicial set $\operatorname{Sing}_{\bullet }(X)$ is connected, then the topological space $X$ is path connected and therefore connected. Beware that the converse is not necessarily true: there exist topological spaces $X$ which are connected but not path connected, in which case the singular simplicial set $\operatorname{Sing}_{\bullet }(X)$ will not be connected.