Closed ideals in topological algebras: a characterization of the topological \(\Phi \)-algebra \(C_k(X)\). (English) Zbl 1164.46339

Montalvo, F.; Pulgarín, A. A.; Requejo, B.

Czech. Math. J. 56, No. 3, 903-918 (2006).

Summary: Let \(A\)  be a uniformly closed and locally m-convex \(\Phi \)-algebra. We obtain internal conditions on  \(A\) stated in terms of its closed ideals for  \(A\) to be isomorphic and homeomorphic to  \(C_k(X)\), the \(\Phi \)-algebra of all the real continuous functions on a normal topological space  \(X\) endowed with the compact convergence topology.

MSC:

46H15	Representations of topological algebras
54H12	Topological lattices, etc. (topological aspects)
06B30	Topological lattices

Keywords:

locally m-convex algebra; \(\Phi \)-algebra; compact convergence topology

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