Strict topologies as topological algebras. (English) Zbl 0983.46025

Summary: Let \(X\) be a completely regular Hausdorff space, \(C_{b}(X)\) the space of all scalar-valued bounded continuous functions on \(X\) with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally \(m\)-convex.


46E10 Topological linear spaces of continuous, differentiable or analytic functions
46H05 General theory of topological algebras
46E25 Rings and algebras of continuous, differentiable or analytic functions
46G10 Vector-valued measures and integration
28B05 Vector-valued set functions, measures and integrals
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
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