For most American writing, stick with no spaces. If you're writing for a British audience or following a specific style guide that allows for spaces, feel free to include them.

Traditionally, curly (or so-called “smart”) quotes have had a use distinct from straight (also called “regular” or the not-so-nice “dumb”) quotes. Pairs of the former are used to enclose quoted material—and they’re “smart” enough to know when to open a quote and when to close it, hence the moniker—while the latter should be reserved for, say, the s

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