Vol. 60, No. 2, 1975

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B-complete and Br-complete topological algebras

Domenico Rosa

Vol. 60 (1975), No. 2, 199–208

In this note, a topological algebra A is an algebra over the field of complex numbers together with a Hausdorff locally convex topology which makes multiplication jointly continuous. A is called B-complete (Br-complete) if every continuous (continuous, one-to-one) and almost open algebra homomorphism from A onto any topological algebra is open. For a completely regular space X, C(X) is the algebra of all continuous complex-valued functions with the usual pointwise operations and the compact-open topology. The main theorem states that C(X) is a B-complete algebra iff X is a k-space.

Mathematical Subject Classification 2000
Primary: 46H20
Secondary: 46A30
Received: 6 February 1975
Published: 1 October 1975
Domenico Rosa