The purpose of this note is to introduce a natural Marinescu structure [7] (an inductive limit of locally convex topological vector spaces in the category of convergence spaces) on C(X) , where C(X) denotes the IR-algebra of all continuous real-valued function on a completely regular topological space X. The structure in question is closely related to Cc(X) , the algebra C(X) endowed with the continuous convergence structure [1].
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