Let 𝐶[0,1] denote the set of all real valued continuous functions defined on [0,1] and ‖𝑓‖_∞ = sup{|𝑓(𝑥)| ∶ 𝑥 ∈ [0,1]} for all 𝑓 ∈ 𝐶[0,1]. Let

𝑋 = { 𝑓 ∈ 𝐶[0,1] ∶ 𝑓(0) = 𝑓(1) = 0 }.

Define 𝐹 ∶ (𝐶[0,1], ‖⋅‖_∞) → ℝ by 𝐹(𝑓) = \(\rm \int_0^1f(t)dt\) for all 𝑓 ∈ 𝐶[0,1].

Denote 𝑆_𝑋 = {𝑓 ∈ 𝑋 ∶ ‖𝑓‖_∞ = 1}.

Then the set {𝑓 ∈ 𝑋 ∶ 𝐹(𝑓) = ‖𝐹‖} ∩ 𝑆_𝑋 has