The Experts below are selected from a list of 249 Experts worldwide ranked by ideXlab platform
Patrick J. Morandi - One of the best experts on this subject based on the ideXlab platform.
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Order-Compactifications of Totally Ordered Spaces: Revisited
Order, 2011Co-Authors: Guram Bezhanishvili, Patrick J. MorandiAbstract:Order-compactifications of totally Ordered Spaces were described by Blatter (J Approx Theory 13:56–65, 1975) and by Kent and Richmond (J Math Math Sci 11(4):683–694, 1988). Their results generalize a similar characterization of order-compactifications of linearly Ordered Spaces, obtained independently by Fedorcuk (Soviet Math Dokl 7:1011–1014, 1966; Sib Math J 10:124–132, 1969) and Kaufman (Colloq Math 17:35–39, 1967). In this note we give a simple characterization of the topology of a totally Ordered Space, as well as give a new simplified proof of the main results of Blatter (J Approx Theory 13:56–65, 1975) and Kent and Richmond (J Math Math Sci 11(4):683–694, 1988). Our main tool will be an order-topological modification of the Dedekind-MacNeille completion. In addition, for a zero-dimensional totally Ordered Space X, we determine which order-compactifications of X are Priestley order-compactifications.
C. A. Rogers - One of the best experts on this subject based on the ideXlab platform.
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Continuous Functions on Totally Ordered Spaces That Are Compact in Their Order Topologies
Journal of Functional Analysis, 2000Co-Authors: Richard Haydon, J. E. Jayne, I. Namioka, C. A. RogersAbstract:Abstract The totally Ordered Spaces that are compact and connected in their order topologies are characterized as images of lexicographic cubes. The Banach Space of continuous functions on the lexicographic product of compact totally Ordered Spaces, whose Spaces of continuous functions have locally uniformly convex norms, has an equivalent locally uniformly convex norm if; and only if, the product is countable. The Banach Space of continuous functions on a compact totally Ordered Space always has an equivalent Kadec norm. Those compact totally Ordered Spaces, for which the Banach Space of continuous functions has an equivalent locally uniformly convex norm, are characterized in terms of the bounded decreasing interval functions that can be defined on the intervals of the totally Ordered Spaces. Some examples are discussed in detail.
Guram Bezhanishvili - One of the best experts on this subject based on the ideXlab platform.
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Order-Compactifications of Totally Ordered Spaces: Revisited
Order, 2011Co-Authors: Guram Bezhanishvili, Patrick J. MorandiAbstract:Order-compactifications of totally Ordered Spaces were described by Blatter (J Approx Theory 13:56–65, 1975) and by Kent and Richmond (J Math Math Sci 11(4):683–694, 1988). Their results generalize a similar characterization of order-compactifications of linearly Ordered Spaces, obtained independently by Fedorcuk (Soviet Math Dokl 7:1011–1014, 1966; Sib Math J 10:124–132, 1969) and Kaufman (Colloq Math 17:35–39, 1967). In this note we give a simple characterization of the topology of a totally Ordered Space, as well as give a new simplified proof of the main results of Blatter (J Approx Theory 13:56–65, 1975) and Kent and Richmond (J Math Math Sci 11(4):683–694, 1988). Our main tool will be an order-topological modification of the Dedekind-MacNeille completion. In addition, for a zero-dimensional totally Ordered Space X, we determine which order-compactifications of X are Priestley order-compactifications.
T. M. Al-shami - One of the best experts on this subject based on the ideXlab platform.
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Compactness on Soft Topological Ordered Spaces and Its Application on the Information System
Journal of Mathematics, 2021Co-Authors: T. M. Al-shamiAbstract:It is well known every soft topological Space induced from soft information system is soft compact. In this study, we integrate between soft compactness and partially Ordered set to introduce new types of soft compactness on the finite Spaces and investigate their application on the information system. First, we initiate a notion of monotonic soft sets and establish its main properties. Second, we introduce the concepts of monotonic soft compact and Ordered soft compact Spaces and show the relationships between them with the help of examples. We give a complete description for each one of them by making use of the finite intersection property. Also, we study some properties associated with some soft Ordered Spaces and finite product Spaces. Furthermore, we investigate the conditions under which these concepts are preserved between the soft topological Ordered Space and its parametric topological Ordered Spaces. In the end, we provide an algorithm for expecting the missing values of objects on the information system depending on the concept of Ordered soft compact Spaces.
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On soft topological Ordered Spaces
Journal of King Saud University - Science, 2019Co-Authors: T. M. Al-shami, M. E. El-shafei, M. Abo-elhamayelAbstract:Abstract In this paper, the authors initiate a soft topological Ordered Space by adding a partial order relation to the structure of a soft topological Space. Some concepts such as monotone soft sets and increasing (decreasing) soft operators are presented and their main properties are studied in detail. The notions of Ordered soft separation axioms, namely p-soft T i -Ordered Spaces ( i = 0 , 1 , 2 , 3 , 4 ) are introduced and the relationships among them are illustrated with the help of examples. In particular, the equivalent conditions for p-soft regularly Ordered Spaces and soft normally Ordered Spaces are given. Moreover, we define the soft topological Ordered properties and then verify that the property of being p-soft T i -Ordered Spaces is a soft topological Ordered property, for i = 0 , 1 , 2 , 3 , 4 . Finally, we investigate the relationships between soft compactness and some Ordered soft separation axioms and point out that the condition of soft compactness is sufficient for the equivalent between p-soft T 2 -Ordered Spaces and p-soft T 3 -Ordered Spaces.
Richard G. Wilson - One of the best experts on this subject based on the ideXlab platform.
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Reflecting properties in continuous images of small weight
European Journal of Mathematics, 2016Co-Authors: Ofelia T. Alas, Lucia R. Junqueira, Richard G. WilsonAbstract:A topological property $$\mathscr {P}$$ P is reflected in continuous images of weight at most $$\omega _1$$ ω 1 if a Space X has $$\mathscr {P}$$ P whenever every continuous image of X of weight at most $$\omega _1$$ ω 1 has $$\mathscr {P}$$ P . When X is a generalized Ordered Space, we consider a number of topological properties including feeble Lindelöfness and $$\kappa $$ κ -monolithicity. In the final section we study small images of pseudocompact and countably compact Spaces; we give a condition on continuous images of a pseudocompact Space in order that it be compact and show that it is consistently true that a countably compact Space of countable projective tightness is countably tight.
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Reflections in small continuous images of Ordered Spaces
European Journal of Mathematics, 2015Co-Authors: Vladimir V. Tkachuk, Richard G. WilsonAbstract:We prove that countable i-weight reflects in continuous images of weight \(\le \omega _1\) for all Tychonoff Spaces while separability reflects in continuous images of weight \(\le \omega _1\) for GO Spaces. If X is a GO Space and all continuous images of X of weight \(\le \kappa ^+\) have tightness at most \(\kappa \), then \(\mathrm{t}{(X)\le \kappa }\). All continuous images of weight \(\le \omega _1\) of a GO Space X have countable pseudocharacter if and only if X is hereditarily Lindelof. Besides, all continuous images of weight \(\le \omega _1\) of a linearly Ordered Space X have \(G_\delta \)-diagonal if and only if X second countable.
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Topologies on totally Ordered sets
Topology and its Applications, 1998Co-Authors: Ralph Kopperman, E. H. Kronheimer, Richard G. WilsonAbstract:Abstract A well-formed Ordered Space is a totally Ordered set equipped with any topology which possesses a subbase consisting entirely of initial and final segments of the set. The well-formed Ordered Spaces are the structures obtained by repeatedly taking subSpaces, quotient Spaces and inverse limits, starting from a collection of totally Ordered sets with the interval topology, and the paper studies their properties.