A digital analogue of the Jordan curve theorem

DOI10.1016/j.dam.2002.11.003zbMath1062.54001OpenAlexW2081819469MaRDI QIDQ1827823

Josef Šlapal

Publication date: 6 August 2004

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2002.11.003

zbMATH Keywords

digital topologyJordan curveKhalimsky topology\(n\)-ary relationKhalimsky plane

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Topological spaces and generalizations (closure spaces, etc.) (54A05)

Related Items (13)

An intuitionistic proof of a discrete form of the Jordan curve theorem formalized in Coq with combinatorial hypermaps ⋮ Another approach to connectedness with respect to a closure operator ⋮ Terse walk sets in graphs and induced closure operators ⋮ Graphs with a path partition for structuring digital spaces ⋮ A Jordan Curve Theorem in the Digital Plane ⋮ Galois connections between sets of paths and closure operators in simple graphs ⋮ Convenient adjacencies for structuring the digital plane ⋮ A quotient-universal digital topology ⋮ Alexandroff pretopologies for structuring the digital plane ⋮ Unnamed Item ⋮ Jordan Curve Theorems with Respect to Certain Pretopologies on $\mathbb Z^2$ ⋮ A Jordan curve theorem with respect to a pretopology on ℤ² ⋮ Unnamed Item

Cites Work

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• Semi-metrics, closure spaces and digital topology
• Boundaries in digital planes
• Computer graphics and connected topologies on finite ordered sets
• A Jordan surface theorem for three-dimensional digital spaces
• Closure operations for digital topology.
• A theory of binary digital pictures
• Digital Topology
• A Topological Approach to Digital Topology
• A converse to the Jordan curve theorem for digital curves
• A GALOIS CORRESPONDENCE BETWEEN CLOSURE SPACES AND RELATIONAL SYSTEMS
• Connectivity in Digital Pictures

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