Take the 2-minute tour ×  I was wondering if anyone could offer
some intuition for why Alexander duality holds. Of course, the
proof is easy enough to check, and it is also easy to work out
many examples by hand. However, I don't have any feeling for why
it is true.  To give you an example of what I am looking for,
when I think of Poincare duality I think of the picture in terms
of triangulations and dual triangulations. Is there any picture
like that for Alexander duality? Is there at least maybe some
kind of obvious bilinear pairing between the two sides of it or
something?  share|improve this question You prove Alexander
duality by a standard combination of Poincare duality and
excision. So if you have intuition for one, you have it for the
other. –  Ryan Budney Oct 13 '10 at 5:28 In particular you can
interpret it in terms of regular neighbourhoods, bounding
cycles, dual triangulations, etc. –  Ryan Budney Oct 13 '10 at
6:02 Dear Ryan, My answer below is essentially an elaboration on
your comment, which I