Results 161 to 170 of about 707 (188)

Identifying key genes in cancer networks using persistent homology. [PDF]

Sci Rep
Ramos RH, Bardelotte YA, de Oliveira Lage Ferreira C, Simao A.   +3 more
europepmc   +1 more source

Enhancing energy predictions in multi-atom systems with multiscale topological learning.

J Mater Chem A Mater
Chen D, Wang R, Wei GW, Pan F.
europepmc   +1 more source

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The Vietoris topology on rectifiable spaces

Semigroup Forum, 2013
In this paper the hyperspace \(C(G)\) of compact subsets of a rectifiable space \(G\) endowed with the Vietoris topology is studied. It is shown that this topological space is a right loop if and only if the cardinality of \(G\) is 1 and that, for a locally compact rectifiable space \(G\), the semi-right loop \(C(G)\) is a topological semi-right loop.
Fucai Lin, Lin Fucai
exaly   +3 more sources

Selections for Vietoris-Like Hyperspace Topologies

Proceedings of the London Mathematical Society, 2000
The authors prove a selection theorem for a Vietoris-like hyperspace topology related to a special clopen base \({\mathcal B}\) of a space \(X\): Theorem 2.1 Let \(X\) be a completely metrizable space which has a clopen \({\mathcal D}\)-orderable base for some \({\mathcal D}\subseteq{\mathcal F}(x)\) (\({\mathcal F}(x)\) denoting the non-empty closed ...
Valentin Gutev, Tsugunori Nogura
exaly   +2 more sources

Continuity properties and Alexandroff theorem in Vietoris topology

Fuzzy Sets and Systems, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alina Gavrilut
exaly   +2 more sources

Reconstruction of the vietoris topology from compacta in the space of closed subgroups

Ukrainian Mathematical Journal, 1990
See the review in Zbl 0702.22009.
A G Piskunov
exaly   +2 more sources

Nonstandard development of the vietoris topology

Lecture Notes in Mathematics, 1991
exaly   +2 more sources

Generalized metric properties on hyperspaces with the Vietoris topology

Rocky Mountain Journal of Mathematics, 2021
The paper investigates the hyperspace of the compact subsets, as well as of the finite subsets of a \(T_3\)-space \(X\) endowed with the Vietoris topology having subbase elements that hit open subsets of \(X\), and miss closed subsets of \(X\), respectively.
Lin, Fucai, Shen, Rongxin, Liu, Chuan
openaire   +2 more sources

A Mayer–Vietoris Formula for Persistent Homology with an Application to Shape Recognition in the Presence of Occlusions [PDF]

Foundations of Computational Mathematics, 2011
In algebraic topology it is well known that, using the Mayer–Vietoris sequence, the homology of a space X can be studied by splitting X into subspaces A and B and computing the homology of A, B, and A∩B.
Barbara Di Fabio, Claudia Landi, Landi Claudia   +2 more
exaly   +3 more sources

Normal Vietoris Implies Compactness: A Short Proof [PDF]

Czechoslovak Mathematical Journal, 2004
summary:One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko).
Meccariello, E., Naimpally, S., Maio, G. Di   +2 more
exaly   +2 more sources