- #1
davidge
- 554
- 21
The unit closed disk minus the point ##(0,0)##
##\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)##?
##\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)##?