whats an infinite intersection of open sets? how is it different from finite intersection of open sets and why is it a closed set in the case of ∞ intersection but open in case of finite. To quote kingwinner, is it being defined as a limit? it really does look look like a limit in the case of ∞ intersections, as in the sets are tending towards their intersection but not actually attaining it . Consider the intersection of the sets ∞ π (1-1/n, 2+ 1/n) n=1 would the smallest set be an infinitesimally small ε on either side of the closed set [1,2], which would hence be their infinite intersection?