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Preservation of properties of a map by forcing

Akira Iwasa (2022)

Commentationes Mathematicae Universitatis Carolinae

Let f : X Y be a continuous map such as an open map, a closed map or a quotient map. We study under what circumstances f remains an open, closed or quotient map in forcing extensions.

Probabilistic approach spaces

Gunther Jäger (2017)

Mathematica Bohemica

We study a probabilistic generalization of Lowen's approach spaces. Such a probabilistic approach space is defined in terms of a probabilistic distance which assigns to a point and a subset a distance distribution function. We give a suitable axiom scheme and show that the resulting category is isomorphic to the category of left-continuous probabilistic topological convergence spaces and hence is a topological category. We further show that the category of Lowen's approach spaces is isomorphic to...

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.

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,...

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