-
Title: Quotient Spaces
-
Series: Manifolds
-
YouTube-Title: Manifolds 4 | Quotient Spaces
-
Bright video: https://youtu.be/nh-YgZph-r4
-
Dark video: https://youtu.be/sXdQg1on3J4
-
Ad-free video: Watch Vimeo video
-
Quiz: Test your knowledge
-
Dark-PDF: Download PDF version of the dark video
-
Print-PDF: Download printable PDF version
-
Thumbnail (bright): Download PNG
-
Thumbnail (dark): Download PNG
-
Subtitle on GitHub: mf04_sub_eng.srt missing
-
Other languages: German version
-
Timestamps (n/a)
-
Subtitle in English (n/a)
-
Quiz Content
Q1: Let $X$ be a set and $\sim$ be an equivalence relation on $X$. What is not a property of $\sim$?
A1: $x \sim x$ for all $x \in X$
A2: If $x \sim y$, then also $y \sim x$
A3: If $x \sim y$ or $x \sim z$, then also $y \sim z$.
A4: If $x \sim y$ and $y \sim z$, then also $x \sim z$.
Q2: Let $(X, \mathcal{T}) $ be a topological space and $\sim$ be an equivalence relation on $X$. What is the definition of the canonical projection $q$?
A1: $q(x) = [x]_{\sim}$
A2: $q([x]_{\sim}) = x$
A3: $q(x) = X/_{\sim}$
Q3: Let $(X, \mathcal{T}) $ be a topological space and $\sim$ be an equivalence relation on $X$. What is the definition of the quotient topology on $X/_{\sim}$?
A1: A set $U$ in $X/_{\sim}$ is open if $q[U]$ is open in $X$.
A2: A set $U$ in $X/_{\sim}$ is open if $q^{-1}[U]$ is open in $X$.
A3: A set $U$ in $X/_{\sim}$ is open if $q[U]$ is not open in $X$.
-
Last update: 2024-10
