\(\varepsilon \)-connectedness, finite approximations, shape theory and coarse graining in hyperspaces
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Publication:1000697
DOI10.1016/j.physd.2008.05.016zbMath1165.54005OpenAlexW2084230705MaRDI QIDQ1000697
Eduardo Cuchillo-Ibanez, Ana Luzón, Manuel Alonso-Morón
Publication date: 10 February 2009
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physd.2008.05.016
data analysisshape theoryVietoris-Rips complex\(\varepsilon \)-connectednessAlexandroff-McCord correspondenceupper semifinite hyperspaces
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Cites Work
- Pointed shape and global attractors for metrizable spaces
- Shift equivalence in homotopy
- Upper semifinite hyperspaces as unifying tools in normal Hausdorff topology
- Homotopical properties of upper semifinite hyperspaces of compacta
- The shape of a cross-section of the solution funnel of an ordinary differential equation
- Shape theory. An introduction
- Global attractors: Topology and finite-dimensional dynamics
- Computing connectedness: disconnectedness and discreteness.
- Shape of global attractors in topological spaces
- Fundamental properties of \(\varepsilon\)-connected sets
- On the structure of uniform attractors
- On the global structure of invariant regions of flows with asymptotically stable attractors
- Singular homology groups and homotopy groups of finite topological spaces
- Every Attractor of a Flow on a Manifold has the Shape of a Finite Polyhedron
- A note about the shape of attractors of discrete semidynamical systems
- Strong cellularity and global asymptotic stability
- An Intrinsic Description of Shape
- Computing connectedness: An exercise in computational topology
- Multihomotopy, Čech Spaces of loops and Shape Groups
- Morse equations and unstable manifolds of isolated invariant sets
- Shape and Morse theory of attractors
- Dynamical systems, shape theory and the Conley index
- THE HAUSDORFF METRIC AND CLASSIFICATIONS OF COMPACTA
- Topology and dynamics of unstable attractors
- Barcodes: The persistent topology of data
- Finite Topological Spaces
- Concerning homotopy properties of compacta
- Shapes for topological spaces
- Topologies on Spaces of Subsets
- Some duality properties of non-saddle sets
- Finite approximations to Čech homology
- Vietoris-Rips complexes of metric spaces near a closed Riemannian manifold
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