Problems and remarks on contractibility of curves
We solve the long standing problem of characterizing the class of strongly Fréchet spaces whose product with every strongly Fréchet space is also Fréchet.
Every nontrivial countably productive coreflective subcategory of topological linear spaces is -productive for a large cardinal (see [10]). Unlike that case, in uniform spaces for every infinite regular cardinal , there are coreflective subcategories that are -productive and not -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...
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,...
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.