Partially paratopological groups / Cenap Özel, Artur Piękosz, Mohammed Al Shumrani, Eliza Wajch // Topology and its Applications [Dokument elektroniczny]. – 2017, Vol. 228, s. 68-78. – Tryb dostępu: ... więcej

Partially paratopological groups / Cenap Özel, Artur Piękosz, Mohammed Al Shumrani, Eliza Wajch // Topology and its Applications [Dokument elektroniczny]. – 2017, Vol. 228, s. 68-78. – Tryb dostępu: http://www.sciencedirect.com/science/article/pii/S0166864117302742. – Bibliogr. 15 poz., Abstr. – doi: 10.1016/j.topol.2017.05.006. – ISSN 0166-8641

In this paper, we introduce the notion of a partially (para)topological group, using generalized topology in the sense of H. Delfs and M. Knebusch. We study some basic properties of this kind of structures. ... więcej

In this paper, we introduce the notion of a partially (para)topological group, using generalized topology in the sense of H. Delfs and M. Knebusch. We study some basic properties of this kind of structures. Among them, we prove that an important theorem of Banakh and Ravsky, applied to their proof in ZFC that every regular paratopological group is completely regular, can be false in a model for ZF. Therefore, it is an open problem whether there exists a model for ZF in which a Hausdorff topological group need not be completely regular. We notice that Banakh–Ravsky theorem that every regular paratopological group is completely regular is provable in every model for ZF+DCZF+DC.