A Fundamental System of Seminorms for A(K)

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Let K⊂ᵈ be compact and A(K) the space of germs of real analytic functions on K with its natural (LF)-topology. This topology can be given by A(K)=ₖ→₊∞ Aₖ where Aₖ={(fα)α∈₀ᵈ∈ C(K)⁰ᵈ: fₖ:=ₓ∈ ₖ |f⁽α⁾(x)|α! k⁻|α|< +∞}. Based on this description we give in the present note an explicit fundamental system of seminorms for A(K).