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Connectedness classes
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: G. CastelliniLet X be an (E,M)-category for sinks. A recently introduced notion of connectedness with respect to a closure operator C on X and to a class of X-monomorphisms N is further analyzed. The notion of N-connectedness hull of a class... -
Closure Operator Constructions Depending On One Parameter
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: G. Castellini D. HolgateLet X be an (E , M)-category for sinks. For each subclass N of M, two new Galois connections that generalize the Clementino-Tholen connectedness and separation Galois connections are introduced. In particular, closure operator constructions that generalize the regular and... -
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,... -
T 1-separation in a category
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: G. CastelliniA general notion of T 1-separation with respect to a closure operator is introduced in an arbitrary category. This is done by specializing a previously introduced diagram of Galois connections. This naturally yields a dual notion of T 1-coseparation. These... -
Interior Operators and Topological Connectedness
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: G. Castellini --- Department of Mathematical Sciences, U.S.A. J. Ramos --- Department of Mathematical Sciences, U.S.A.A categorical notion of interior operator is used in topology to define connectedness and disconnectedness with respect to an interior operator. A commutative diagram of Galois connections is used to show a relationship between these notions and Arhangelskii and Wiegandt's... -
Discrete Objects, Splitting Closure and Connectedness
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Gabriele CastelliniNotions of discrete and indiscrete classes with respect to a closure operator are introduced and studied. These notions are strongly related to splitting and cosplitting closure operators. By linking the above concepts, two Galois connections arise whose composition provides a... -
The geometry of the moduli space of non-cyclic biquadratic field extensions
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Mpendulo Cele --- Stellenbosch University, South Africa Sophie Marques --- Stellenbosch University, South AfricaIn this paper, we investigate the existence of an elementary abelian closure in characteristic not 2 for biquadratic extensions. We discover that it exists for any non-cyclic extension. We make use of it to obtain a classification for this class... -
Some questions on partially ordered rings – a survey
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jingjing Ma --- University of Houston-Clear Lake, USAThis survey provides a brief overview and new developments on some questions in the area of partially ordered and lattice-ordered rings and algebras.