Topology · Lesson 06
Ten questions across the chapter, with no teaching blocks. Products are described three ways — by a subbasis, by a basis of boxes and by a metric — and choosing the convenient description is the skill being practised.
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Sign in to save progressTen questions across the chapter, with no teaching blocks. Products are described three ways — by a subbasis, by a basis of boxes and by a metric — and choosing the convenient description is the skill being practised.
One road can be described by its junctions, its stretches or its length. Which description to reach for depends on the question asked.
The chapter in four lines.
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What is the subbasis that defines the product topology?
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Which subset of the plane is open in the product topology, although it is not a box?
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A projection of a product is an open map.
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A projection of a product is a closed map.
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. Which condition is equivalent to continuity of ?
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In with the maximum metric, what is the distance between and ?
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Which family is a basis for the product topology on ?
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A map out of a product that is continuous in each variable separately is continuous.
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Which metric on has balls that are exactly the basic boxes?
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In a product of infinitely many spaces, how many coordinates does a basic open set restrict?