Displaying similar documents to “A note on Fréchet-Urysohn locally convex spaces.”

Metrizability of precompact sets: an elementary proof.

J. C. Ferrando, J. Kakol, M. López Pellicer (2005)

RACSAM

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Proporcionamos una demostración muy corta de un teorema de Cascales-Orihuela que establece que todo conjunto precompacto de un espacio localmente convexo de la clase G (en el sentido de Cascales-Orihuela) es metrizable.

Factorization of Montel operators

S. Dierolf, P. Domański (1993)

Studia Mathematica

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Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given. ...

Two-fold theorem on Fréchetness of products

Szymon Dolecki, Tsugunori Nogura (1999)

Czechoslovak Mathematical Journal

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A refined common generalization of known theorems (Arhangel’skii, Michael, Popov and Rančin) on the Fréchetness of products is proved. A new characterization, in terms of products, of strongly Fréchet topologies is provided.