Topology · Lesson 07
Twelve questions across the chapter, with no teaching blocks. Continuity has three equivalent tests and two directions, and deciding which one a question is really about is the practice here.
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Sign in to save progressTwelve questions across the chapter, with no teaching blocks. Continuity has three equivalent tests and two directions, and deciding which one a question is really about is the practice here.
A driving test does not announce which manoeuvre is coming. Recognising the situation is most of the skill.
The chapter in five lines.
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A map sends every point of to a single point of . Is it continuous?
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Which of these fails to prove that is continuous?
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For on , what is ?
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A map continuous at every point of its domain is continuous.
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is continuous and . What can be said about ?
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Two continuous maps are glued along a shared boundary. When is the result continuous?
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A continuous bijection is a homeomorphism.
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Which property would prove two spaces are not homeomorphic?
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is a two-point discrete space and a two-point indiscrete space. How many continuous maps go from to ?
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is a continuous open bijection. What follows?
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It is enough to check the preimages of the members of a subbasis of the target.
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Which maps into a discrete space are continuous?