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narrow eyes; half-open eyes
fine mesh; fine texture; tight weave; smooth cut (of a file)
「細目」 has another reading with different meanings.
祖母は細目で孫を見た。
The grandmother looked at her grandchild with narrow eyes.
授業中、彼は眠そうに細目になった。
During class, he became sleepy and his eyes narrowed.
日差しの中で猫が気持ちよさそうに細目を開けた。
The cat opened its eyes narrowly, looking very comfortable in the sunlight.