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taken up is an adjective meaning "having or showing excessive or compulsive concern with something". It carries one recorded sense.
having or showing excessive or compulsive concern with something
“became more and more haunted by the stupid riddle”
“was absolutely obsessed with the girl”
“got no help from his wife who was preoccupied with the children”
“he was taken up in worry for the old woman”
Definitions, synonyms and semantic relations for taken up come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.