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When describing fluid flows, does the term "incompressible" mean exactly the same thing as "constant density"?

I was under the impression that if a fluid cannot be compressed, then its density must remain constant for any fixed volume of fluid. My textbook intriguingly says "For an incompressible fluid (including the case of constant density), divergence is zero." This wording seems to suggest you can have an incompressible fluid which does not have constant density...

Can anyone elucidate?

Thanks in advance