-regular Cauchy completions.
-topological Cauchy completions.
Partial dcpo’s and some applications
We introduce partial dcpo’s and show their some applications. A partial dcpo is a poset associated with a designated collection of directed subsets. We prove that (i) the dcpo-completion of every partial dcpo exists; (ii) for certain spaces , the corresponding partial dcpo’s of continuous real valued functions on are continuous partial dcpos; (iii) if a space is Hausdorff compact, the lattice of all S-lower semicontinuous functions on is the dcpo-completion of that of continuous real valued...
Pointless uniformities. I. Complete regularity
Pointless uniformities. II: (Dia)metrization
Pointwise convergence fails to be strict
It is known that the ring of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of which differs from .
Polars on closure spaces
Précompactologies et structures uniformes
Presheaves over the sets which need not be well ordered, functional separation of their inductive limits and their representation by sections
Prime extensions and nearness structures
Prime filters with CIP
Probabilistic convergence spaces and generalized metric spaces.
Probabilistic convergence spaces and regularity.
Producto, convexificación y completación de espacios métricos generalizados y probabilísticos.
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 locally connected locales
Properties of some -dense-in-itself subsets.
Properties of some generalizations of the notion of continuity of a function
Properties of -closed sets in topological spaces
In questo articolo vengono presentate e studiate le nozioni di insieme e di insieme -chiuso. Inoltre, vengono introdotte le nozioni di -continuità, -compatezza e -connessione e vengono fornite alcune caratterizzazioni degli spazi e . Infine, viene mostrato che gli spazi -connessi e -compatti vengono preservati mediante suriezioni -continue.