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A strict topology for some weighted spaces of continuous functions


Abstract


In the classical case the strict topology \beta introduced by Buck [2] on the space C^b(X) of bounded continuous scalar valued functions on the locally compact Hausdorff space X is given by the system W of all weights on X that vanish at infinity. The \beta-bounded subsets of C^b(X) are exactly the norm bounded subsets, and \beta is the finest locally convex topology which coincides on the norm bounded subsets with the compact open topology (cf. Dorroh [4]). Especially we have that C^b (X) = CW(X) = CW_0 (X) holds algebraically. In this note we want to describe for an arbitrary system of weights V an associated system of weights W such that at least in many cases, including the classical one, the connection between CV(X) and CW_0 (X) is the same as in the classical case.

DOI Code: 10.1285/i15900932v11p135

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