Reading through the book "The Shape of Space" by Jeffrey Weeks, I encountered the claim that the two surfaces (a) and (f) in the following picture has the same "extrinsic topology" 
To say that two surfaces have the same extrinsic topology is very loosely defined, and is the same as saying that they can be deformed to eachother. I am having trouble seeing how to resolve the "knot" in (f). Could anyone help me with some visual guidance for why this (f) has the same extrinsic topology as (a)?
** Let me be clear: I agree that the surfaces clearly are homeomorphic. But to me, "extrinsic topology" seems to say that they are isotopic in the $3$-space, or something similar. If so, can anyone explain why this is the case?