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Striking differences between ZF and ZF+weak choice in view of metric spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Horst Herrlich Kyriakos Keremedis Eleftherios TachtsisWell-known properties held by metric spaces with the countable chain condition (ccc) such as separability, second countability, Lindelöf, paracompactness may fail in the absence of the axiom of choice AC. In the long catalogue of weak choice principles, see [10],... -
Function spaces and d-separability
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: VladimirV. TkachukThe object of this paper is to study when a function space is d-separable, i.e., has a dense σ-discrete subspace. Several sufficient conditions are obtained for C p(X) to be d-separable; as an application it is proved that C p(X)... -
Aspects of nearness in σ-frames
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Inderasan NaidooWe introduce the notion of a nearness on a σ-frame. The concept of strong nearness for a σ-frame is intermediate between those of nearness and uniformity and we show that the category of strong nearness σ-frame SN σ Frm is... -
Isomorphisms into section spaces of Banach bundles
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Terje Hõim D.A. RobbinsLet X be a compact Hausdorff space, E a (real) Banach space, and let C(X, E) be the space of continuous functions from X to E. The monograph of Cembranos and Mendoza provides a primer on when C (X, E)... -
Rotundity in transitive and separable Banach spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: A. Aizpuru F.J. García-PachecoIn every separable Banach space the set of smooth points of the unit ball is a Gδ dense subset of the unit sphere. In this paper, we find some conditions in order to obtain a similar result for rotund points... -
On Weaker Forms of Separability
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Maddalena Bonanzinga Filippo Cammaroto Mikhail Matveev Bruno PanseraTwo properties each of which is equivalent to separability for regular spaces and is weaker than separability in general are considered as well as the corresponding cardinal functions.