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 {\displaystyle \left} 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 ∞ { ∈ R 2 ∣ 2 + y 2 = 2 } {\displaystyle \mathbb {H} =\bigcup _{n=1}^{\infty }\left\{\in \mathbb {R} ^{2}\mid \left^{2}+y^{2}=\left^{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. Wikipedia