Topology · Lesson 08
Fourteen questions across the whole course, with no teaching blocks. The course began with a distance and ended with spaces built by gluing, and every step in between was made in open sets alone. These questions are drawn from all nine chapters.
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Sign in to save progressFourteen questions across the whole course, with no teaching blocks. The course began with a distance and ended with spaces built by gluing, and every step in between was made in open sets alone. These questions are drawn from all nine chapters.
A last walk through a building you helped put up: the point is not the walls, it is knowing which of them hold the roof.
What the nine chapters established.
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Which family of subsets of a set is never a topology on it?
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Every topological space comes from a metric.
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What is the closure of in ?
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Which condition defines continuity of a map between topological spaces?
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A continuous image of a compact space is compact.
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For which spaces does "compact" mean "closed and bounded"?
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Which subsets of are connected?
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A convergent sequence in a Hausdorff space cannot have two different limits.
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Which space is T1 and not Hausdorff?
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How many connected components has ?
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What must a second countable space have?
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When is a subset of a quotient space open?
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Gluing the two ends of a closed interval gives a space homeomorphic to the interval.
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An argument runs: " is a continuous bijection, so and are homeomorphic." What is missing?