• Title/Summary/Keyword: Galois connection

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THE STRUCTURE OF GALOIS CONNECTION IN FUZZY ORDERED SETS

  • Lee
    • Journal of applied mathematics & informatics
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    • v.6 no.1
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    • pp.247-252
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    • 1999
  • The purposed of this paper is to introduced some basic concepts of Galois connection between fuzzy ordered sets. And discuss its relations with the property of fuzzy ordered set.

Pointless Form of Rough Sets

  • FEIZABADI, ABOLGHASEM KARIMI;ESTAJI, ALI AKBAR;ABEDI, MOSTAFA
    • Kyungpook Mathematical Journal
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    • v.55 no.3
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    • pp.549-562
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    • 2015
  • In this paper we introduce the pointfree version of rough sets. For this we consider a lattice L instead of the power set P(X) of a set X. We study the properties of lower and upper pointfree approximation, precise elements, and their relation with prime elements. Also, we study lower and upper pointfree approximation as a Galois connection, and discuss the relations between partitions and Galois connections.

M-SCOTT CONVERGENCE AND M-SCOTT TOPOLOGY ON POSETS

  • Yao, Wei
    • Honam Mathematical Journal
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    • v.33 no.2
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    • pp.279-300
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    • 2011
  • For a subset system M on any poset, M-Scott notions, such as M-way below relation,M-continuity,M-Scott convergence (of nets and filters respectively) and M-Scott topology are proposed Any approximating auxiliary relation on a poset can be represented by an M-way below relation such that this poset is M-continuous. It is shown that a poset is M-continuous iff the M-Scott topology is completely distributive. The topology induced by the M-Scott convergence coincides with the M-Scott topology. If the M-way below relation satisfies the property of interpolation then a poset is M-continuous if and only if the M-Scott convergence coincides with the M-Scott topological convergence. Also, M-continuity is characterized by a certain Galois connection.

REGULAR MAPS-COMBINATORIAL OBJECTS RELATING DIFFERENT FIELDS OF MATHEMATICS

  • Nedela, Roman
    • Journal of the Korean Mathematical Society
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    • v.38 no.5
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    • pp.1069-1105
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    • 2001
  • Regular maps and hypermaps are cellular decompositions of closed surfaces exhibiting the highest possible number of symmetries. The five Platonic solids present the most familar examples of regular maps. The gret dodecahedron, a 5-valent pentagonal regular map on the surface of genus 5 discovered by Kepler, is probably the first known non-spherical regular map. Modern history of regular maps goes back at least to Klein (1878) who described in [59] a regular map of type (3, 7) on the orientable surface of genus 3. In its early times, the study of regular maps was closely connected with group theory as one can see in Burnside’s famous monograph [19], and more recently in Coxeter’s and Moser’s book [25] (Chapter 8). The present-time interest in regular maps extends to their connection to Dyck\`s triangle groups, Riemann surfaces, algebraic curves, Galois groups and other areas, Many of these links are nicely surveyed in the recent papers of Jones [55] and Jones and Singerman [54]. The presented survey paper is based on the talk given by the author at the conference “Mathematics in the New Millenium”held in Seoul, October 2000. The idea was, on one hand side, to show the relationship of (regular) maps and hypermaps to the above mentioned fields of mathematics. On the other hand, we wanted to stress some ideas and results that are important for understanding of the nature of these interesting mathematical objects.

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