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Title: Continuity
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Series: Manifolds
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YouTube-Title: Manifolds 7 | Continuity
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Bright video: https://youtu.be/oPsiD2Vyd_Y
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Dark video: https://youtu.be/-keH0IwZlxQ
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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: mf07_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 a topological space and $f: X \rightarrow X$ be a map given by $f(x) = x$ for all $x \in X$. Is the map continuous?
A1: Yes, always!
A2: No, never!
A3: It depends on the topology $\mathcal{T}$.
Q2: Let $(X,\mathcal{T})$ be the discrete topological space. What is always correct for every map $f: X \rightarrow X$?
A1: $f$ is continuous.
A2: $f$ is not sequentially continuous.
A3: $f$ is constant.
Q3: Let $(X,\mathcal{T}_X)$ and $(Y,\mathcal{T}_Y)$ be two topological spaces and $f: X \rightarrow Y$ be a continuous map. Is $f$ also sequentially continuous?
A1: Yes, always!
A2: No, never!
A3: Only if $(X,\mathcal{T}_X)$ is given by a metric space.
A4: Only if $(Y,\mathcal{T}_Y)$ is a second-countable space.
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Last update: 2024-10
