In this post, I’ll talk about Alexander Duality, one of my favorite results in algebraic topology. I’ll defer the proof to a subsequent blog post; in this one, I’ll state the theorem and discuss some immediate consequences of interest.
The setup is as follows: let be a nonempty, compact subset of the -sphere such that there exists an open neighborhood which deformation retracts to , and such that is an -manifold with boundary.
Theorem (Alexander duality)
Comments
w theorem vro
This is very cool theorem!