RT Journal Article
T1 Conway’s Question: The Chase for Completeness
A1 Dikranjan, Dikran
A1 Martín Peinador, Elena
A1 Tarieladze, Vaja
AB We study various degrees of completeness for a Tychonoff space X. One of them plays a central role, namely X is called a Conway space if X is sequentially closed in its Stone–Čech compactification β X (a prominent example of Conway spaces is provided by Dieudonné complete spaces). The Conway spaces constitute a bireflective subcategory Conw of the category Tych of Tychonoff spaces. Replacing sequential closure by the general notion of a closure operator C, we introduce analogously the subcategory Conw C of C-Conway spaces, that turns out to be again a bireflective subcategory of Tych. We show that every bireflective subcategory of Tych can be presented in this way by building a Galois connection between bireflective subcategories of Tych and closure operators of Top finer than the Kuratowski closure. Other levels of completeness are considered for the (underlying topological spaces of) topological groups. A topological group G is sequentially complete if it is sequentially closed in its Raĭkov completion . The sequential completeness for topological groups is stronger than Conway’s property, although they coincide in some classes of topological groups, for example: free (Abelian) topological groups, pseudocompact groups, etc.
PB Springer Verlag
SN 0927-2852
YR 2007
FD 2007
LK https://hdl.handle.net/20.500.14352/49679
UL https://hdl.handle.net/20.500.14352/49679
LA eng
NO Grupo Santander (in the program Estancias de Doctores y Tecnólogos Extranjeros en la U.CM.).
NO MCYT
NO FEDER
DS Docta Complutense
RD 30 abr 2024