The Greek eidōleion refers to an idol temple — the physical structure housing idol worship. Paul uses it in 1 Corinthians 8:10 in his discussion of food sacrificed to idols: 'For if someone with a weak conscience sees you, with all your knowledge, eating in an idol's temple (eidōleion), won't that person be emboldened to eat what is sacrificed to idols?' The location matters — eating in the eidōleion itself signals participation in idol worship beyond mere food.
Paul's argument in 1 Corinthians 8-10 about eidōleion is nuanced. The strong know an idol is nothing (1 Corinthians 8:4) — but reclining at table in an idol temple could ensnare weaker brothers (8:10-11) or inadvertently constitute fellowship with demons (10:20-21). Knowledge without love causes harm. The freedom to know that idols are nothing does not grant freedom to participate in spaces devoted to their worship. The church's separation from the eidōleion was not because the idols were real but because of what such spaces signified socially and spiritually.