Proof: Let W ∈ ℬ. Set K = { 0 } and C = W^{C}. Then C is closed set and K is compact set and C ∩ K = Ф.

Hence ∃ a neighborhood V of 0 such that (C+ V) ∩ (K+V) = Ф.

Since B is a local base ∃ U∈ ℬ such that U ⊂ V.

(C+ U) ∩ (K+U) = Ф.

Thus (C+ U) ∩ U = Ф. [∵K+U = U]

and hence __U __∩C+ U = Ф

Since C⊂ C + U, __U __∩C = Ф

⟹ __U__⊂ C^{C}

⟹ __U__⊂ W (Proved)