Search
Search results for
We found
8 results for you
-
Irreducibility in Pointfree Topology
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Themba DubeIrreducible spaces have been studied in topology by several authors. A. H. Stone introduced semi-irreducibility as a way of studying hereditarily compact spaces. In this paper we investigate these concepts in the context of frames. -
The Galois Approach to Uniform Structures
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Maria João Ferreira Jorge PicadoEntourages in uniform spaces, being binary relations, may be easily described by polarities (i.e. Galois connections between power sets) and axialities (i.e. residuated pairs between power sets). Here we consider this in the pointfree context of the category of frames,... -
Frame presentations of compact hedgehogs and their properties
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Igor Arrieta --- University of Coimbra, Portugal Javier Gutiérrez García --- University of the Basque Country UPV/EHU, Spain Jorge Picado --- University of Coimbra, PortugalThis paper considers the compact hedgehog as a frame presented by generators and relations, based on the presentation of the frame of extended real numbers. The main focus will be on the point-free version of continuous and semi-continuous functions that... -
On the categorical behaviour of locales and D-localic maps
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Igor Arrieta --- University of Coimbra, Portugal Javier Gutiérrez García --- University of the Basque Country UPV/EHU, SpainIt was shown by Banaschewski and Pultr that the classical adjunction between Top and Loc restricts to an adjunction between the category Top D of TD -spaces and their continuous maps, and the category Loc D of all locales and... -
Remote sublocales
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Mbekezeli Nxumalo --- University of South Africa, South AfricaWe use the notion of a remote collection of a Tychonoff space to define a remote sublocale of any locale. Our definition is conservative, in the sense that, a subset is remote if and only if the sublocale it induces... -
Notes on sublocales and dissolution
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jorge Picado --- University of Coimbra, Portugal Aleš Pultr --- Charles University, Czech RepublicThe dissolution (introduced by Isbell in [3], discussed by Johnstone in [5] and later exploited by Plewe in [12, 13]) is here viewed as the relation of the geometry of L with that of the more dispersed T(L) = S(L)op... -
On variants and generalizations of J-frames
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Siyabonga S. Dubazana --- University of KwaZulu-Natal, S.A. Simo S. Mthethwa --- University of KwaZulu-Natal, S.A.A J-frame is a pointfree topology counterpart of the concept of a J-space. In this paper, we present a study of some frames satisfying conditions that are stronger (and some that are weaker) than those defining J-frames. Conditions under which... -
On quotient rings of pointfree function rings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Batsile Tlharesakgosi --- University of South Africa, South Africa Sharon Nyokabi Wamugunda --- University of South Africa, South AfricaLet L be a completely regular frame. Associated with each I ∈ βL are two ideals, MI and OI , of the ring of real-valued continuous functions on a frame L. In this paper, we describe the intersection of all...