Let X be a completely regular Hausdorff space and let E be a real locally convex Hausdorff space. Katsaras  has studied the topologies β0, β, and β1, for the vector-valued case on Crc(X,E), the space of all continuous E-valued functions on X with relatively compact range. The corresponding dual spaces are the spaces Mt (B,E'), Mτ (B,E'), and M (B,E') of all t-additive, all τ-additive, and all σ-additive members of M(B,E'), the dual space of Crc (X,E') under the uniform topology. In this paper we study the subspace Me(B,E') of M(B,E'). A locally convex topology βe is defined on Crc(X,E) that yields Me (B,E') as a dual space. It is proved that if E is strongly Mackey then (C (X,E),βe) is strongly Mackey.
Dual Space Hausdorff Space Uniform Topology Convex Topology Continuous Seminorm
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