If exp ⁡ ( X i ) ∖ { ∅ } \exp ({X_i})\backslash \{ \emptyset \} is equipped with a topology that preserves the topological convergence of nets of sets for every i ∈ I i \in I , then the Tychonoff product of the family { exp ⁡ ( X i ) ∖ { ∅ } : i ∈ I } \{ \exp ({X_i})\backslash \{ \emptyset \} :i \in I\} is compact if and only if X i {X_i} is compact for every i ∈ I i \in I . A similar result concerning sequential compactness is valid, for countable I.