Topology · Lesson 07
Twelve questions across the chapter, with no teaching blocks. Connectedness is shown by transport and disconnectedness by example, and knowing which of the two a question is asking for is half of answering it.
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Sign in to save progressTwelve questions across the chapter, with no teaching blocks. Connectedness is shown by transport and disconnectedness by example, and knowing which of the two a question is asking for is half of answering it.
A search party proves a wood empty by covering it, and proves it occupied by finding one person. Which job you are on decides how you walk.
The chapter in five lines.
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Which pair separates the real line without 0?
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A space has a subset that is open, closed, non-empty and not the whole space. What follows?
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Which of these subsets of is connected?
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Two connected sets with no point in common have a connected union.
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is continuous and onto, and is connected. What follows about ?
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A continuous map sends onto , and is both compact and connected. What follows about ?
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Does compact imply connected, or connected imply compact?
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Every connected space is path connected.
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How many components has the subspace of ?
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An argument runs: " is connected, because between any two rationals there is another." Where does it go wrong?
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Every connected component is closed, and every one is open.
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Which of these is a topological invariant?