 For each possible "direction" in which points in R"n" can "escape", one new point at infinity is added (but each direction is identified with its opposite).The Alexandroff one-point compactification of R we constructed in the example above is in fact homeomorphic to RP1.Note however that the projective plane RP2 is "not" the one-point compactification of the plane R2 since more than one point is added.