Path Connectedness

Let M be a set endowed with the topology T.
It is said that A ⊂ M is Path connected if there exists a continuous path between two given points of M, or also,

∀ x1, x2 ∈ M, ∃ Γ: [0,1] → M such as Γ(x1)=0, Γ(x2)=1

Note: All topological space Path connected is connected. The converse is not true.

In addition the property is connected by road a topological property, ie it is preserved by homeomorphisms, ie if M is space topological path connected and F is homoemorfismo, then F (M) is path connected