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In page Connected space:

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A space X {\displaystyle X} is said to be arc-connected or arcwise connected if any two topologically distinguishable points can be joined by an arc, which is an embedding f : [ 0 , 1 ] X {\displaystyle f:[0,1]\to X} .[citation needed] An arc-component of X {\displaystyle X} is a maximal arc-connected subset of X {\displaystyle X} ; or equivalently an equivalence class of the equivalence relation of whether two points can be joined by an arc or by a path whose points are topologically indistinguishable.