The Khalimsky topologies are precisely those simply connected topologies on \(\mathbb Z^n\) whose connected sets include all 2\(n\)-connected sets but no (3\(^{n}-1\))-disconnected sets.
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Publication:1427781
DOI10.1016/S0304-3975(02)00710-7zbMath1072.68110OpenAlexW2018797100MaRDI QIDQ1427781
Publication date: 14 March 2004
Published in: Theoretical Computer Science (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0304-3975(02)00710-7
Khalimsky spaceDigital topologyMetric analogMultidimensionalPolyhedral analogSimply connected topology
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Shy maps in topology ⋮ Strongly normal sets of contractible tiles in \(n\) dimensions ⋮ The fixed point property of the infinite K-sphere in the set Con*((Z2)*) ⋮ Homotopy equivalence which is suitable for studying Khalimsky \(n\)D spaces ⋮ Paths, homotopy and reduction in digital images ⋮ Unnamed Item ⋮ Continuous digitization in Khalimsky spaces ⋮ On storage of topological information ⋮ Uniqueness of the perfect fusion grid on \(\mathbb{Z}^d\) ⋮ Topological graphs based on a new topology on Zn and its applications
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- Topological adjacency relations on \(Z^{n}\)
- Weak lighting functions and strong 26-surfaces.
- Homotopy in two-dimensional digital images
- Singular homology groups and homotopy groups of finite topological spaces
- Connectivity in Digital Pictures
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