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Characterization of posets for order-convergence being topological

  • Tao Sun EMAIL logo und Qingguo Li
Veröffentlicht/Copyright: 9. Februar 2018
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 68 Heft 1

Abstract

We study a basic problem: in what posets is the order-convergence topological? We introduce the notion of 𝓡∗-doubly continuous posets, which extends the notion of doubly continuous posets, and then prove that the order-convergence in a poset is topological if and only if the poset is 𝓡∗-doubly continuous. This is the main result which can be regarded as a complete characterization of posets for the order-convergence being topological.

MSC 2010: Primary 06A06; 54A20
Keywords: poset; order-convergence; topology; doubly continuous poset; 𝓡∗-doubly continuous poset

This work was supported by the Natural Science Foundation of China, Grant No. 11371130, and the Natural Science Foundation of Guangxi, Grant No. 2014GXNSFBA118015.

Communicated by L’ubica Holá

Acknowledgements

We would like to thank the anonymous referee and Prof. Vladimír Olejček for their careful reading and valuable comments which have improved the quality of this paper.

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Received: 2015-10-23
Accepted: 2016-5-30
Published Online: 2018-2-9
Published in Print: 2018-2-23

© 2018 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

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  4. Characterization of posets for order-convergence being topological
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  8. On a generalized concept of order relations on B(H)
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https://doi.org/10.1515/ms-2017-0075
Schlagwörter fĂŒr diesen Artikel
poset; order-convergence; topology; doubly continuous poset; 𝓡∗-doubly continuous poset

Artikel in diesem Heft

  2. On the number of cycles in a graph
  4. Characterization of posets for order-convergence being topological
  6. Classification of posets using zero-divisor graphs
  8. On a generalized concept of order relations on B(H)
  10. A study of stabilizers in triangle algebras
  12. Revealing two cubic non-residues in a quadratic field locally
  14. Codensity and stone spaces
  16. Big mapping class groups are not acylindrically hyperbolic
  18. Applications of Henstock-Kurzweil integrals on an unbounded interval to differential and integral equations
  20. Starlike and convex functions with respect to symmetric conjugate points involving conical domain
  22. Summations of Schlömilch series containing anger function terms
  24. Some vector valued sequence spaces of Musielak-Orlicz functions and their operator ideals
  26. Nuclear operators on Cb(X, E) and the strict topology
  28. More on cyclic amenability of the Lau product of Banach algebras defined by a Banach algebra morphism
  30. Matrix generalized (Ξ, ϕ)-derivations on matrix Banach algebras
  32. Nonlinear ∗-Jordan triple derivations on von Neumann algebras
  34. Addendum to “A sequential implicit function theorem for the chords iteration”, Math. Slovaca 63(5) (2013), 1085–1100
  36. Comparison of density topologies on the real line
  38. Rational homotopy of maps between certain complex Grassmann manifolds
  40. Examples of random fields that can be represented as space-domain scaled stationary Ornstein-Uhlenbeck fields
  42. Rothe’s method for physiologically structured models with diffusion
  44. Zero-divisor graphs of lower dismantlable lattices II
  46. An identity of symmetry for the degenerate Frobenius-Euler Polynomials
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