The unit closed disk minus the point ##(0,0)##(adsbygoogle = window.adsbygoogle || []).push({});

##\mathbb{D}^1 \setminus (0,0): \bigg[(x,y) \in \mathbb{R}^2 | 0 < x^2 + y^2 \leq 1 \bigg]##

is homeomorphic to the unit circle

##\mathbb{S}^1: \bigg[(x,y) \in \mathbb{R}^2 | x^2 + y^2 = 1 \bigg]##

Since ##\mathbb{D}^1 = \big(\mathbb{D}^1 \setminus (0,0) \big) \cup (0,0)##, is it correct to say that

##\mathbb{D}^1 \sim \mathbb{S}^1 \cup (0,0)##?

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# I The disk and the circle

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