Let X=(x,y)inR^2:x^2+y^2<1cup(x,y)inR^2:(x-2)^2+y^2<1 and Y=(x,y)inR^2:x^2+y^2<1cup(x,y)inR^2:(x-3)^2+y^2<1 and Z=(x,y)inR^2:x^2+y^2<1, xneq0 be subspaces of the Euclidean space R^2. Then:

(A) X and Y are homeomorphic to Z

Q60Section II (Mathematics)60 of 190

Two components of an open disc each, regardless of gap size or how the split arises, are all homeomorphic

Let $X=\{(x,y)\in\mathbb{R}^2:x^2+y^2<1\}\cup\{(x,y)\in\mathbb{R}^2:(x-2)^2+y^2<1\}$ and $Y=\{(x,y)\in\mathbb{R}^2:x^2+y^2<1\}\cup\{(x,y)\in\mathbb{R}^2:(x-3)^2+y^2<1\}$ and $Z=\{(x,y)\in\mathbb{R}^2:x^2+y^2<1, x\neq0\}$ be subspaces of the Euclidean space $\mathbb{R}^2$ . Then:

Pick an option to check your answer.

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