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Les topologies sygma-Lebesgue sur C(X).

Belmesnaoui Aqzzouz, Redouane Nouira (2004)

Extracta Mathematicae

We prove that if X is a compact topological space which contains a nontrivial metrizable connected closed subset, then the vector lattice C(X) does not carry any sygma-Lebesgue topology.

Limited spaces

N. De Grande-De Kimpe, C. Perez-Garcia (1995)

Annales mathématiques Blaise Pascal

Linear topological invariants of spaces of holomorphic functions in infinite dimension.

Nguyen Minh Ha, Le Mau Hai (1995)

Publicacions Matemàtiques

It is shown that if E is a Frechet space with the strong dual E* then Hb(E*), the space of holomorphic functions on E* which are bounded on every bounded set in E*, has the property (DN) when E ∈ (DN) and that Hb(E*) ∈ (Ω) when E ∈ (Ω) and either E* has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V) consisting of holomorphic functions on E* which are equal to 0 on V in H(E*) for every nuclear Frechet space E with E ∈ (DN) ∩ (Ω) is stablished...

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