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Productively Fréchet spaces

Francis Jordan, Frédéric Mynard (2004)

Czechoslovak Mathematical Journal

We solve the long standing problem of characterizing the class of strongly Fréchet spaces whose product with every strongly Fréchet space is also Fréchet.

Productivity of coreflective classes of topological groups

Horst Herrlich, Miroslav Hušek (1999)

Commentationes Mathematicae Universitatis Carolinae

Every nontrivial countably productive coreflective subcategory of topological linear spaces is κ -productive for a large cardinal κ (see [10]). Unlike that case, in uniform spaces for every infinite regular cardinal κ , there are coreflective subcategories that are κ -productive and not κ + -productive (see [8]). From certain points of view, the category of topological groups lies in between those categories above and we shall show that the corresponding results on productivity of coreflective subcategories...

Producto, convexificación y completación de espacios métricos generalizados y probabilísticos.

Claudi Alsina (1978)

Stochastica

En 1967 E. Trillas introdujo la noción de espacio métrico generalizado, al considerar métricas abstractas valoradas en semigrupos ordenados, unificando con este punto de vista algebraico-reticular las estructuras métricas reales de M. Fréchet ([5]) y los espacios métricos probabilísticos de K. Menger ([6]) (así como los espacios Booleanos de Blumenthal ([4]) y las métricas naturales definidas en grupos ordenados). En el presente artículo se abordan los problemas de la topología del orden, del producto,...

Products of Baire spaces revisited

László Zsilinszky (2004)

Fundamenta Mathematicae

Generalizing a theorem of Oxtoby, it is shown that an arbitrary product of Baire spaces which are almost locally universally Kuratowski-Ulam (in particular, have countable-in-itself π-bases) is a Baire space. Also, partially answering a question of Fleissner, it is proved that a countable box product of almost locally universally Kuratowski-Ulam Baire spaces is a Baire space.

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