  It is a classical theorem of Alexandroff that a locally compact Hausdorff
space has a one-point Hausdorff compactification if and only if it is
non-compact. The one-point Hausdorff compactification is indeed obtained by
adding the so called "point at infinity." Here we consider the analogous
problem of existence of a one-point connectification, and keeping analogy, we
prove that a locally connected normal space has a one-point normal
connectification if and only if it has no compact component.
