I have a question? Why is it that every subset of a metric space is a metric space? I mean what if the subset is the empty set, then it can't be a metric space, right? because a metric space is by definition a non-empty set. So would I be correct to say that every non-empty subset of a metric space is a metric space? But i'm confused because since compact sets are metric spaces, and every finite set is a compact set, doesn't that mean that the empty set is compact? Therefore a metric space by definition?
2026-04-04 14:16:48.1775312208
Subset of a metric space is a metric space.
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I think a metric space can be empty, see Wikipedia.