[ColinWright]

The surface is simply connected, it's the outside that ends up not being simply connected. This works equally well with piece-wise linear embeddings. And the current version of the Alexander Horned Sphere is not actually interlocking - the embedding is contractable back to S^2.

It takes a while to get your head around what this really is.

[tehwalrus]

OK, "proximate" rather than interlocking. I did understand the geometry of it, I just chose the wrong word. Thanks for your explanations! :)