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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... -
Approach structures and measures of connectedness
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: David Holgate Mark SioenMeasures of connectedness versus disconnectedness are introduced in anarbitrary topological construct as fixed points of a Galois connection. This places measures of connectedness found in the literature in a general categorical frame-work. -
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 significance of the contributions of congruences to the theory of connectednesses and disconnectednesses for topological spaces and graphs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Stefan Veldsman --- Nelson Mandela University, South AfricaThis is a survey of some of the consequences of the recently introduced congruences on the theory of connectednesses (radical classes) and disconnectednesses (semisimple classes) of graphs and topological spaces. In particular, it is shown that the connectednesses and disconnectednesses...