Hawaiian earring
In mathematics, the Hawaiian earring H {\displaystyle \mathbb {H} } is the topological space defined by the union of circles in the Euclidean plane R 2 {\displaystyle \mathbb {R} ^{2}} with center ( 1 n , 0 ) {\displaystyle \left({\tfrac {1}{n}},0\right)} and radius 1 n {\displaystyle {\tfrac {1}{n}}} for n = 1 , 2 , 3 , … {\displaystyle n=1,2,3,\ldots } endowed with the subspace topology: H = ⋃ n = 1 ∞ { ( x , y ) ∈ R 2 ∣ ( x − 1 n ) 2 + y 2 = ( 1 n ) 2 } . {\displaystyle \mathbb {H} =\bigcup _{n=1}^{\infty }\left\{(x,y)\in \mathbb {R} ^{2}\mid \left(x-{\frac {1}{n}}\right)^{2}+y^{2}=\left({\frac {1}{n}}\right)^{2}\right\}.} The space H {\displaystyle \mathbb {H} } is homeomorphic to the one-point compactification of the union of a countable family of disjoint open intervals.