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For each $n \in \mathbb{N}$, define the circle $S_n$, which passes through the origin by: $$S_n := \left\{ (x,y) \in \mathbb{R}^2 : x^2+\left(y-\tfrac{1}{n}\right)^2=\tfrac{1}{n^2}\right\}$$ I know that the union of all $S_n$ is taken as the base space for some topological space. Can anyone remember the name and/or supply a link? I think it has the word earrings in the title.

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I dub this topological space "Steve." Most people call it the Hawaiian earring, though. –  Cameron Buie Dec 16 '13 at 16:18
    
Ha ha ha! Thanks @CameronBuie that's the one. –  Fly by Night Dec 16 '13 at 16:35

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I believe you're thinking of the Hawaiian earring.

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...Also known as "Steve" –  Omnomnomnom Dec 16 '13 at 16:22
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...I think I prefer Steve. –  Fly by Night Dec 16 '13 at 16:35

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