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Zheyuan Wu
2026-01-14 13:52:17 -06:00
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@@ -14,4 +14,10 @@ Classifying two dimensional surfaces.
## Quotient spaces
Let $X$ be a topological space and $f:X\to Y$ is a continuous, surjective map. WIth the property that $U\subset Y$ is open if and only if $f^{-1}(U)$ is open in $X$, we say $f$ is a quotient map and $Y$ is a quotient space.
Let $X$ be a topological space and $f:X\to Y$ is a
1. continuous
2. surjective map.
3. With the property that $U\subset Y$ is open if and only if $f^{-1}(U)$ is open in $X$.
Then we say $f$ is a quotient map and $Y$ is a quotient space.