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.
Jerzy Kakol (2004)
Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales
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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. ...
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.
Bonet, J., Dierolf, S., Fernández, C. (1992)
Portugaliae mathematica
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Sunday Gluyemi (1997)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Pedro Pérez Carreras (1987)
Časopis pro pěstování matematiky
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Aleksander V. Arhangel'skii (2010)
Commentationes Mathematicae Universitatis Carolinae
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Some strong versions of the Fréchet-Urysohn property are introduced and studied. We also strengthen the concept of countable tightness and generalize the notions of first-countability and countable base. A construction of a topological space is described which results, in particular, in a Tychonoff countable Fréchet-Urysohn space which is not first-countable at any point. It is shown that this space can be represented as the image of a countable metrizable space under a continuous pseudoopen...