cosmopolitan has 8 distinct synonyms spread across 3 of its 4 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its 2 recorded opposites are endemic, provincial.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
growing or occurring in many parts of the world
“a cosmopolitan herb”
composed of people from or at home in many parts of the world; especially not provincial in attitudes or interests
“his cosmopolitan benevolence impartially extended to all races and to all creeds”
of worldwide scope or applicability
“an issue of cosmopolitan import”
a sophisticated person who has travelled in many countries
Synonyms, antonyms and the broader and narrower relations for cosmopolitan come from Princeton University’s WordNet. Full sources and licences.