Extremally Disconnected Spaces

Terasawa, Jun

doi:10.1016/b978-044450355-8/50092-1

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Cited by 2 publications

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“…This gives rise to the (apparently) obvious Jordan curve theorem, which says that every Jordan curve divides the plane into an "interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior points. Therefore, in topology, despite the analytic description of disconnected sets has been extensively provided (Arkhangelskii 2001;Terasawa, 2004), we are in front of a rather simple statement: there exist an "inside" and an "outside" region.…”

Section: Discussionmentioning

confidence: 99%

Topological Assessment of Unidentified Moving Objects

Tozzi¹,

Peters²

2019

Preprint

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Starting from unidentified objects moving inside a two-dimensional Euclidean manifold, we propose a simple method to detect the topological changes that occur during their reciprocal interactions and shape morphing. This method, which allows the detection of topological holes development and disappearance, makes it possible to solve the uncertainty due to disconnectedness, lack of information and absence of objects' sharp boundaries, i.e., the three troubling issues which prevent scientists to select the required proper sets/subsets during their experimental assessment of natural and artificial dynamical phenomena, such as fire propagation, wireless sensor networks, migration flows, neural networks' and cosmic bodies' analysis.

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Section: Discussionmentioning

confidence: 99%