Results 11 to 20 of about 82 (77)
Preorderable topologies and order-representability of topological spaces
Topology and its Applications, 2009 A total preorder is called continuous (resp. semicontinuous) with respect to a given topology provided that the order topology (resp. lower or upper topology) induced by the total preorder is coarser than the given topology. Topologies that coincide with the order topology (resp.
Campión, María Jesús +2 more
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Some utility theorems on inductive limits of preordered topological spaces [PDF]
Bulletin of the Australian Mathematical Society, 1995 We prove the existence of an order-preserving function on a class of preordered topological spaces that are inductive limits of preordered spaces. Some applications to economics are given.
Candeal, J. C. +2 more
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Order extension of order monomorphisms on a preordered topological space [PDF]
International Journal of Mathematics and Mathematical Sciences, 1993 The well-known extension theorem of \textit{L. Nachbin} [Topology and order (1965; Zbl 0131.379), p. 36] gives conditions under which a real-valued continuous order-homomorphism defined on a closed subset of a normally preordered space \(E\) can be extended to a real-valued continuous order- homomorphism on the whole space.
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Extension of Kirk‐Saliga Fixed Point Theorem in a Metric Space with a Reflexive Digraph
International Journal of Mathematics and Mathematical Sciences, Volume 2018, Issue 1, 2018., 2018 We extend the result of Kirk‐Saliga and we generalize Alfuraidan and Khamsi theorem for reflexive graphs. As a consequence, we obtain the ordered version of Caristi’s fixed point theorem. Some concrete examples are given to support the obtained results.
Karim Chaira +4 more
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Multiobjective Optimization, Scalarization, and Maximal Elements of Preorders
Abstract and Applied Analysis, Volume 2018, Issue 1, 2018., 2018 We characterize the existence of (weak) Pareto optimal solutions to the classical multiobjective optimization problem by referring to the naturally associated preorders and their finite (Richter‐Peleg) multiutility representation. The case of a compact design space is appropriately considered by using results concerning the existence of maximal ...
Paolo Bevilacqua +3 more
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Representation embeddings, interpretation functors and controlled wild algebras
Journal of the London Mathematical Society, Volume 94, Issue 3, Page 747-766, December 2016., 2016 We establish a number of results which say, roughly, that interpretation functors preserve algebraic complexity. First, we show that representation embeddings between categories of modules of finite‐dimensional algebras induce embeddings of lattices of pp formulas, and hence are non‐decreasing on Krull–Gabriel dimension and uniserial dimension.
Lorna Gregory, Mike Prest
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Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 We apply the extensions of the Abian‐Brown fixed point theorem for set‐valued mappings on chain‐complete posets to examine the existence of generalized and extended saddle points of bifunctions defined on posets. We also study the generalized and extended equilibrium problems and the solvability of ordered variational inequalities on posets, which are ...
Jinlu Li, Ying Liu, Hongya Gao, Chong Li
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Generalized Contractive Set‐Valued Maps on Complete Preordered Quasi‐Metric Spaces
Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013 By using a suitable modification of the notion of a w‐distance we obtain some fixed point results for generalized contractive set‐valued maps on complete preordered quasi‐metric spaces. We also show that several distinguished examples of non‐metrizable quasi‐metric spaces and of cones of asymmetric normed spaces admit w‐distances of this type.
J. Marín +3 more
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Moment Problems on Bounded and Unbounded Domains
International Journal of Analysis, Volume 2013, Issue 1, 2013., 2013 Using approximation results, we characterize the existence of the solution for a two‐dimensional moment problem in the first quadrant, in terms of quadratic forms, similar to the one‐dimensional case. For the bounded domain case, one considers a space of complex analytic functions in a disk and a space of continuous functions on a compact interval. The
Octav Olteanu, Zhijun Qiao
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Sequences suffice for pointfree uniform completions
Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.Abstract Completions of metric spaces are usually constructed using Cauchy sequences. However, this does not work for general uniform spaces, where Cauchy filters or nets must be used instead. The situation in pointfree topology is more straightforward: the correct completion of uniform locales can indeed be obtained as a quotient of a locale of Cauchy
Graham Manuell
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