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Last edited by hbghlyj 2023-7-4 11:17Page 10
Example There are homeomorphisms $K＃ℝP^2≅ℝP^2＃ℝP^2＃ℝP^2≅T^2＃ℝP^2$
—The first follows from the previous example. For the second, $ℝP^2＃ℝP^2＃ℝP^2≅S^2＃(ℝP^2)^3$
Regard this as $S^2$ with 3 discs removed, with boundaries glued as shown.
Cut along purple lines into two regions, as shown.
Green region is $ℝP^2∖\text{disc}$
White region is $T^2∖\text{disc}$
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我明白绿色部分连接起来是一条带子扭转$\frac32$圈，所以是Möbius带。
蓝色字不理解：white region为什么是$T^2∖\text{disc}$
white region是去掉3个绿色区域的球面 |
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