 Then "X" has one end for every sequence
where each "U""n" is a connected component of "X" \ "K""n".The number of ends does not depend on the specific sequence {"K""i"} of compact sets; there is a natural bijection between the sets of ends associated with any two such sequences.Using this definition, a neighborhood of an end {"U""i"} is an open set "V" such that "V" ⊃ "U""n" for some "n".