 It follows that a locally connected space "X" is a topological disjoint union formula_25 of its distinct connected components.Conversely, if for every open subset "U" of "X", the connected components of "U" are open, then "X" admits a base of connected sets and is therefore locally connected.Similarly "x" in "X", the set formula_26 of all points "y" such that formula_27 is called the "path component" of "x".