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Title: Projective Space
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Series: Manifolds
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YouTube-Title: Manifolds 5 | Projective Space
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Bright video: https://youtu.be/WstgxuPSxuE
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Dark video: https://youtu.be/zr3vySH6g-A
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Ad-free video: Watch Vimeo video
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: mf05_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: What is the definition of the $n$-dimensional sphere?
A1: $S^n = { x \in \mathbb{R}^{n+1} \mid | x | \leq 1 }$
A2: $S^n = { x \in \mathbb{R}^n \mid | x | \geq 1 }$
A3: $S^n = { x \in \mathbb{R}^{n+1} \mid | x | = 1 }$
A4: $S^n = { x \in \mathbb{R}^{n} \mid | x | = 1 }$
A5: $S^n = { x \in \mathbb{R}^{n+1} \mid | x | \geq 1 }$
Q2: What is the definition of the projective space $\mathbf{P}^n(\mathbb{R})$?
A1: $S^n! /! ! \sim ~~$ for $x\sim y$ if $x=y$.
A2: $S^n! /! ! \sim ~~$ for $x\sim y$ if $x=y$ or $x = -y$.
A3: $S^n! /! !\sim ~~$ for $x\sim y$ if $x=y$ and $x = -y$.
A4: $S^n ! /! ! \sim ~~$ for $x\sim y$ if $x=y-1 $.
Q3: Is the projective space $\mathbf{P}^n(\mathbb{R})$ together with the quotient topology a Hausdorff space?
A1: Yes!
A2: No!
A3: Only for $n=1$.
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Last update: 2024-10
