Zobrazeno 1 - 10
of 1 427
pro vyhledávání: '"Digital topology"'
Autor:
Laurence Boxer
Publikováno v:
Applied General Topology, Vol 25, Iss 2, Pp 457-473 (2024)
This paper continues a series in which we study deficiencies in previously published works concerning fixed point assertions for digital images.
Externí odkaz:
https://doaj.org/article/54ea0680a41f49f0bffd488b0e0c1869
Autor:
Laurence Boxer
Publikováno v:
Applied General Topology, Vol 24, Iss 2, Pp 281-305 (2023)
This paper continues a series discussing flaws in published assertions concerning fixed points in digital metric spaces.
Externí odkaz:
https://doaj.org/article/ce3db201bf1849b9b9c73bafc46006ac
Autor:
Laurence Boxer
Publikováno v:
Applied General Topology, Vol 23, Iss 2, Pp 437-451 (2022)
As in [6, 3, 4, 5], we discuss published assertions concerning fixed points in “digital metric spaces” - assertions that are incorrect or incorrectly proven, or reduce to triviality.
Externí odkaz:
https://doaj.org/article/02686c9b242d45c3b5b5d5158727ed0b
Autor:
Sang-Eon Han
Publikováno v:
Electronic Research Archive, Vol 30, Iss 12, Pp 4341-4365 (2022)
The paper initially develops the semi-Jordan curve theorem on the digital plane with the Marcus-Wyse topology, i.e., $ MW $-topological plane or $ ({\mathbb Z}^2, \gamma) $ for brevity. We first prove that while every simple closed $ MW $-curve is se
Externí odkaz:
https://doaj.org/article/85c71c9563a74eaea02c654c467bff33
Akademický článek
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Akademický článek
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Autor:
Sang-Eon Han
Publikováno v:
AIMS Mathematics, Vol 7, Iss 7, Pp 11581-11596 (2022)
Let $ (X, T) $ be an Alexandroff space. We define the adjacency relation $ AR_T $ on $ X $ induced by $ T $ as the irreflexive relation defined for $ x \neq y $ in $ X $ by: $ (x,y) \in AR_T\,\,{\rm{if \;and\; only\; if}}\,\, x \in SN_T(y)\,\,{\rm
Externí odkaz:
https://doaj.org/article/aee995be86e54ad8a126dfbe9a2e59a1
Autor:
Laurence Boxer
Publikováno v:
Applied General Topology, Vol 23, Iss 1, Pp 69-77 (2022)
Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that objects close in each of these measures have some similar geometric or topo
Externí odkaz:
https://doaj.org/article/5518bb6492a645a19c6ff6c3cfe1e67b
Autor:
Sang-Eon Han
Publikováno v:
Electronic Research Archive, Vol 30, Iss 6, Pp 2356-2384 (2022)
The purpose of the paper is to study digital topological versions of typical topological groups. In relation to this work, given a digital image $ (X, k), X \subset {\mathbb Z}^n $, we are strongly required to establish the most suitable adjacency re
Externí odkaz:
https://doaj.org/article/395241bb5f0a4ffb825c459c8c817bb8
Publikováno v:
AIMS Mathematics, Vol 7, Iss 1, Pp 1224-1240 (2022)
The present paper intensively studies various properties of certain topologies on the set of integers $ {\mathbb Z} $ (resp. $ {\mathbb Z}^n $) which are either homeomorphic or not homeomorphic to the typical Khalimsky line topology (resp. $ n $-dime
Externí odkaz:
https://doaj.org/article/d7f37df97eb8428d86f06ee93d19d584