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Is a set the same thing as a topic?

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As set is a collection of objects.  I've never heard a topic come up in mathematics.  If you regard a topic as a collection of objects, yeah sure, they're the same.  But that would be a weird definition of a topic.  Usually a topic is the focus of some conversation.
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What would "topic of real numbers" even mean? That's not a mathematical notion.
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Sounds like you’re translating something into English.

Topology has a strict mathematical definition that has little to do with the etymology of the word.

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