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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],... -
A Pointfree Study of Bases For Spaces Of Minimal Prime Ideals
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Melvin Henriksen Joanne Walters-WaylandLet C (X) denote the ring of all real-valued continuous functions on a topological space X, and mX its space of minimal prime ideals with the hull-kernel topology. It has a base consisting of clopen sets and which contains the... -
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)... -
On Lindel¨of uniform frames and the axiom of countable choice
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: B. Banaschewski J.L. Walters-WaylandThis paper takes another look at the result that any complete separable uniform frame is Lindelöf and some of its ramifications. In particular, it shows that this is equivalent to the axiom of countable choice and provides a new, considerably... -
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... -
Oz in pointfree topology
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Bernhard Banaschewski Themba Dube Christopher Gilmour Joanne Walters-WaylandOz frames are the natural pointfree counterpart of Oz spaces, that is, those topological spaces in which every open set is z-embedded. We give here the point-free analogues of known characterisations of Oz spaces and show that the Lindelöf coreflection...