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I am new to both subject areas and am currently choosing modules to take next year. I'm pretty certain I want to take topology but metric spaces is currently not on my list. Would it be recommended to take metric spaces as a kind of pre-requisite to topology or am I fine taking just topology. Any information on the role metric spaces play within topology or how integral it is in understanding topology?

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Metric spaces are particularly nice topological spaces. Many topological spaces found “in the wild” are metric spaces. Almost every topological space I work with in my particular field is a metric space.

To answer your questions:

  • Understanding metric spaces is not a prerequisite to understanding topology, although you do learn many topological ideas through studying metric spaces. It can be a good jumping off point to general topology.

  • Conversely, you do not need to understand metric spaces in order have a basic grasp on topology. Most likely, you will learn what a metric space is in your topology class though you won’t go as in depth as your metric spaces class might.

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