A strict topology for some weighted spaces of continuous functions
Abstract
In the classical case the strict topology
introduced by Buck [2] on the space
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
-bounded subsets of
are exactly the norm bounded subsets, and
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
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
and
is the same as in the classical case.
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DOI Code:
10.1285/i15900932v11p135
Full Text: PDF