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Title: Examples for Manifolds
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Series: Manifolds
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YouTube-Title: Manifolds 10 | Examples for Manifolds
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Bright video: https://youtu.be/IsB4JGLPgH0
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Dark video: https://youtu.be/hJIoBmLurF4
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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: mf10_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 $(X,\mathcal{T})$ be the discrete topological space. Is it a manifold?
A1: Yes, always!
A2: No, never!
A3: There are examples and counterexamples.
Q2: Let $(\mathbb{R},\mathcal{T})$ be the topological space given by the discrete topology. Is it a manifold?
A1: Yes!
A2: No!
Q3: Let $(\mathbb{N},\mathcal{T})$ be the topological space given by the discrete topology. Is it a manifold?
A1: Yes!
A2: No!
A3: There is not enough information to answer this question.
Q4: Let $(\mathbb{R},\mathcal{T})$ be the topological space given by the standard topology. This is a manifold of dimension
A1: $0$.
A2: $1$.
A3: $2$.
A4: $3$.
A5: $4$.
Q5: Let $(M,\mathcal{T})$ be a manifold and $(U_i, h_i)_{i \in I}$ an atlas. What is correct?
A1: $\bigcup_{i \in I} U_i = \emptyset$
A2: $\bigcap_{i \in I} U_i = \emptyset$
A3: $\bigcup_{i \in I} U_i = M$
A4: $\bigcap_{i \in I} U_i = M$
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Last update: 2024-10
