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Title: Submanifolds
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Series: Manifolds
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YouTube-Title: Manifolds 14 | Submanifolds
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Bright video: https://youtu.be/0fAlx5HgDfM
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Dark video: https://youtu.be/yn3PFVnL6dg
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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: mf14_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: Let $M$ be a manifold. Is $M$ also a submanifold of $M$?
A1: Yes!
A2: No!
A3: This makes no sense!
Q2: Is the sphere $\mathbb{S}^n$ a submanifold of $\mathbb{R}^{n+1}$?
A1: Yes!
A2: No!
A3: This makes no sense!
Q3: Let $U \subseteq \mathbb{R}^n $ be an open set. Is $U$ a submanifold?
A1: Yes, always and the dimension is $0$.
A2: No, never.
A3: No, only for special cases.
A4: Yes, always and the dimension is $n$.
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Last update: 2024-10
