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Title: Second-Countable Space
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Series: Manifolds
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YouTube-Title: Manifolds 6 | Second-Countable Space
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Bright video: https://youtu.be/ulFi1zsn-yM
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Dark video: https://youtu.be/oyNSWc-ZPrU
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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: mf06_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. What is correct for a base $\mathcal{B}$ of a topology $\mathcal{T}$?
A1: $\mathcal{B} \in \mathcal{T}$
A2: $\mathcal{B} \in X$
A3: $\mathcal{B} \subseteq X$
A4: $\mathcal{B} \subseteq \mathcal{T}$
Q2: Let $(X,\mathcal{T})$ be a topological space. What is always correct for every base $\mathcal{B}$ of a topology $\mathcal{T}$?
A1: Every open set can be written as an intersection of the sets from $\mathcal{B}$.
A2: Every open set can be written as a union of the sets from $\mathcal{B}$.
A3: Every open set can be written as a finite union of the sets from $\mathcal{B}$.
Q3: Does every topological space have a basis?
A1: Yes!
A2: No!
A3: Only if it is the discrete topological space.
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Last update: 2024-10
