# In topological terms, how would you describe the relationship between two consecutive links of a chain?

Consider the two rings that this magician is holding in his hands:

How would you describe that configuration in topological terms?

From a knot-theory standpoint, I would say that the rings form a two-component link that is equivalent to a Hopf link. I'm no knot-theory specialist, though; they're may be a simpler way of putting it.

I'm wondering what technical term is used in topology to describe that type of relationship between such a pair of sets.

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I suspect that the picture does not properly represent the case you have in mind. The two half link will shrink down in to two points and the middle link is a circle. –  Fly by Night May 3 '13 at 18:03
I'll change the picture to more accurately represent what I have in mind. –  Jubobs May 3 '13 at 18:04

"Two (solid, unknotted) tori embedded in $\Bbb R^3$ are linked iff their complement has abelian fundamental group" works. You need to mention the ambient space in some way because without it they're just two separate tori with no relationship with eachother.
If we have one ring $R$, then the other ring is linked with it if it not continuously deformable to a point within $\Bbb R^3\setminus R$. (In this case it's easier if the rings are thought of as circles, rather than tori.)