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Convexity in the Khalimsky Plane

  • Ezzeddine Bouassida EMAIL logo , Riyadh Gargouri und Rim Messaoud
Veröffentlicht/Copyright: 9. Februar 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 65 Heft 6

Abstract

Let ℤ2 be equipped with the Khalimsky topology κ, it is a T0-Alexandroff topology which has some specific properties concerning continuity and connectivity. We define digital-arcs and the geodesics; this enables us to define D-convexity on the digital plane (ℤ2, κ). First, we prove a theorem dealing with the relationship between D-convexity and connectivity. The second result links together the convexity in ℝ2 and the D-convexity in ℤ2. For this purpose, we suggest the continuous digitization of the real line segment and thus prove that the digitization of a convex subset of ℝ2 is a D-convex subset of (ℤ2, κ).

Keywords: Alexandroff space; Khalimsky topology; connectivity; digital arcs; D-convexity; Jordan curves; continuous digitization

References

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Received: 2012-9-25
Accepted: 2013-2-18
Published Online: 2016-2-9
Published in Print: 2015-12-1

Mathematical Institute Slovak Academy of Sciences

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  2. On Primary Ideals in Posets
  3. Characterization of the Set of Regular Elements in Ordered Semigroups
  4. Tame Automorphisms with Multidegrees in the Form of Arithmetic Progressions
  5. A Result Concerning Additive Mappings in Semiprime Rings
  6. Characterizing Jordan Derivations of Matrix Rings Through Zero Products
  7. Existence Results for Impulsive Nonlinear Fractional Differential Equations With Nonlocal Boundary Conditions
  8. The Radon-Nikodym Property and the Limit Average Range
  9. A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
  10. On Booth Lemniscate and Hadamard Product of Analytic Functions
  11. Recursion Formulas for Srivastava Hypergeometric Functions
  12. Regularly Varying Solutions of Half-Linear Diffferential Equations with Retarded and Advanced Arguments
  13. Singular Degenerate Differential Operators and Applications
  14. The Interior Euler-Lagrange Operator in Field Theory
  15. On Selections of Set-Valued Maps Satisfying Some Inclusions in a Single Variable
  16. The Family F of Permutations of ℕ
  17. Summation Process of Positive Linear Operators in Two-Dimensional Weighted Spaces
  18. On Iλ-Statistical Convergence in Locally Solid Riesz Spaces
  19. Some Norm one Functions of the Volterra Operator
  20. Some Results on Absolute Retractivity of the Fixed Points Set of KS-Multifunctions
  21. Convexity in the Khalimsky Plane
  22. Natural Boundary Conditions in Geometric Calculus of Variations
  23. Exponential Inequalities for Bounded Random Variables
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  25. Second Order Riemannian Mechanics
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https://doi.org/10.1515/ms-2015-0104
Schlagwörter für diesen Artikel
Alexandroff space; Khalimsky topology; connectivity; digital arcs; D-convexity; Jordan curves; continuous digitization

Artikel in diesem Heft

  1. Radius, Diameter and the Degree Sequence of a Graph
  2. On Primary Ideals in Posets
  3. Characterization of the Set of Regular Elements in Ordered Semigroups
  4. Tame Automorphisms with Multidegrees in the Form of Arithmetic Progressions
  5. A Result Concerning Additive Mappings in Semiprime Rings
  6. Characterizing Jordan Derivations of Matrix Rings Through Zero Products
  7. Existence Results for Impulsive Nonlinear Fractional Differential Equations With Nonlocal Boundary Conditions
  8. The Radon-Nikodym Property and the Limit Average Range
  9. A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
  10. On Booth Lemniscate and Hadamard Product of Analytic Functions
  11. Recursion Formulas for Srivastava Hypergeometric Functions
  12. Regularly Varying Solutions of Half-Linear Diffferential Equations with Retarded and Advanced Arguments
  13. Singular Degenerate Differential Operators and Applications
  14. The Interior Euler-Lagrange Operator in Field Theory
  15. On Selections of Set-Valued Maps Satisfying Some Inclusions in a Single Variable
  16. The Family F of Permutations of ℕ
  17. Summation Process of Positive Linear Operators in Two-Dimensional Weighted Spaces
  18. On Iλ-Statistical Convergence in Locally Solid Riesz Spaces
  19. Some Norm one Functions of the Volterra Operator
  20. Some Results on Absolute Retractivity of the Fixed Points Set of KS-Multifunctions
  21. Convexity in the Khalimsky Plane
  22. Natural Boundary Conditions in Geometric Calculus of Variations
  23. Exponential Inequalities for Bounded Random Variables
  24. Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of φ-Mixing Sequences
  25. Second Order Riemannian Mechanics
  26. Further Remarks on an Order for Quantum Observables
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