The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
We investigate free groups over sequential spaces. In particular, we show that the free -group and the free sequential group over a sequential space with unique limits coincide and, barred the trivial case, their sequential order is .
In this paper -spaces are introduced and studied. They are a common generalization of Lindelöf spaces and -spaces researched by E. Michael. A space is called an -space if, whenever is a closed cover of with compact, then or is Lindelöf. Semi-strong -spaces and strong -spaces are also defined and investigated. It is demonstrated that the three spaces are different and have interesting properties and behaviors.
We prove that, for every countable ordinal α ≥ 3, there exists
countable completely regular spaces Xα and Yα such that the spaces Cp (Xα )
and Cp (Yα ) are borelian of class exactly Mα , but are not homeomorphic.
Soit une application analytique propre entre des ouverts de , soit un sous-ensemble analytique de et soit . On donne des conditions pour que soit de codimension 1 dans .
Nous nous proposons de rendre à Émile Borel le mérite d’avoir considéré le premier un recouvrement d’un segment de droite par une suite infinie d’intervalles et prouvé que l’on peut en extraire un sous-recouvrement fini. L’appellation de théorème de Heine-Borel souvent donnée à ce résultat, en référence à un article de Heine de 1872, conduit à sous-estimer les différences avec le théorème sur la continuité uniforme (dont une première version peut être attribuée à Dirichlet, en 1854) ; cette dénomination...
If X is a quasitopological space -Spanier space in this paper-, a topological space q X can be associated to X. A subset F of X is called closed if it is closed in q X. Interesting properties of the closed subspaces of a quasitopological space are examined.
Currently displaying 1 –
20 of
198