Given an infinite cardinal \(\kappa \) , we say that a space X has \(\kappa \) -accessible boundaries of its open sets if \(\overline{U} = \bigcup \{\overline{A}: A\in [U]^{\le \kappa }\}\) for every open set \(U\subset X\) . If X has the above-mentioned property for \(\kappa =\omega \) , then X is said to have accessible boundaries of open sets. We show that all spaces \(C_p(X)\) have accessible boundaries of open sets. A GO space X has \(\kappa \) -accessible boundaries of open sets if and only if \(\chi (X) \le \kappa \) . A product \(\prod _{t\in T} X_t\) has \(\kappa \) -accessible boundaries of open sets if and only if the same is true for \(\prod _{t\in A} X_t\) for any \(A\in [T]^{\le \kappa }\) . As a consequence, all products of separable spaces as well as all products of compact spaces of countable tightness have accessible boundaries of open sets.
