Let X=(x,y)inR^2:0lex=yle1, Y=(x,y)inR^2:x+y=1 and Z=(x,y)inR^2:x^2+y^2=1 be subspaces of the Euclidean space R^2. Then:

(C) Y is homeomorphic to Z, but not X

Q60Section II (Mathematics)60 of 190

Two simple closed curves are homeomorphic to each other, but not to a branched "X"

Let $X=\{(x,y)\in\mathbb{R}^2:0\le|x|=|y|\le1\}$ , $Y=\{(x,y)\in\mathbb{R}^2:|x|+|y|=1\}$ and $Z=\{(x,y)\in\mathbb{R}^2:x^2+y^2=1\}$ be subspaces of the Euclidean space $\mathbb{R}^2$ . Then:

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