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Title: Compactness
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Series: Manifolds
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Chapter: Topology
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YouTube-Title: Manifolds 8 | Compactness
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Bright video: Watch on YouTube
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Dark video: Watch on YouTube
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Ad-free video: Watch Vimeo video
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Original video for YT-Members (bright): Watch on YouTube
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Original video for YT-Members (dark): Watch on YouTube
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Forum: Ask a question in Mattermost
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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: mf08_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $(\mathbb{R},\mathcal{T})$ be the topological space given by the discrete topology. Is the set $[0,1]$ compact?
A1: Yes!
A2: No!
A3: There is not enough information to answer this question.
Q2: Let $(\mathbb{R},\mathcal{T})$ be the topological space given by the indiscrete topology. Is the set $[0,1]$ compact?
A1: Yes!
A2: No!
A3: There is not enough information to answer this question.
Q3: Let $(X,\mathcal{T})$ be a Hausdorff space and $A \subseteq X$ a closed set. Is $A$ compact?
A1: Yes!
A2: No!
A3: There is not enough information to answer this question.
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Last update: 2025-09
