Persistent homology for MCI classification: a comparative analysis between graph and Vietoris-Rips filtrations [PDF]
Frontiers in NeuroscienceIntroductionMild cognitive impairment (MCI), often linked to early neurodegeneration, is associated with subtle disruptions in brain connectivity. In this paper, the applicability of persistent homology, a cutting-edge topological data analysis technique
Debanjali Bhattacharya +6 more
doaj +4 more sources
Vietoris topology on spaces dominated by second countable ones
Open Mathematics, 2015 For a given space X let C(X) be the family of all compact subsets of X. A space X is dominated by a space M if X has an M-ordered compact cover, this means that there exists a family F = {FK : K ∈ C(M)} ⊂ C(X) such that ∪ F = X and K ⊂ L implies that FK ⊂
Islas Carlos, Jardon Daniel
doaj +4 more sources
CL(R) is simply connected under the Vietoris topology
Applied General Topology, 2007 In this paper we present a proof by construction that the hyperspace CL(R) of closed, nonemtpy subsets of R is simply connected under the Vietoris topology. This is useful in considering the convergence of time scales.
N.C. Esty
doaj +6 more sources
Entanglement, space-time and the Mayer-Vietoris theorem
Journal of High Energy Physics, 2017 Entanglement appears to be a fundamental building block of quantum gravity leading to new principles underlying the nature of quantum space-time. One such principle is the ER-EPR duality.
Andrei T. Patrascu
doaj +3 more sources
Vietoris topology on hyperspaces associated to a noncommutative compact space [PDF]
Mathematica, 2017 We study some topological spaces that can be considered as hyperspaces associated to noncommutative spaces. More precisely, for a NC compact space associated to a unital C*-algebra, we consider the set of closed projections of the second dual of the C ...
M. M. Sadr
semanticscholar +3 more sources
The upper Vietoris topology on the space of inverse-closed subsets of a spectral space and applications [PDF]
Rocky Mountain Journal of Mathematics, 2018 Given an arbitrary spectral space $X$, we consider the set ${\boldsymbol{\mathcal{X}}}(X)$ of all nonempty subsets of $X$ that are closed with respect to the inverse topology.
C. Finocchiaro, M. Fontana, D. Spirito
semanticscholar +6 more sources
$\omega$ -cover and related spaces on the vietoris hyperspace $\mathcal F(X)$
Tạp chí Khoa học và Công nghệRecently, Tuyen et al. [1] showed that a space has a $\sigma$-(P)-strong network consisting of cs-covers (resp., $cs^*$-covers) if and only if the hyperspace $\mathcal F(X)$ does, where is one of the following properties: point finite, point countable,
Nguyen Xuan Truc +3 more
doaj +2 more sources
Algebraic characterisation of hyperspace corresponding to topological vector space [PDF]
Journal of Hyperstructures, 2023 Let X be a Hausdor topological vector space over the field of real or complex numbers. When Vietoris topology is given,the hyperspace ℘(X) of all nonempty compact subsets of X forms a topological exponential vector space over the same field. Exponential
Jayeeta Saha, Sandip Jana
doaj +1 more source
On some cardinal invariants of space of finite subsets
Lietuvos Matematikos Rinkinys, 2005 In article is investigated relationships between some cardinal invariants of topological space and it’s space of finite subsets with Vietoris topology. In generalwe note coincidence of them.
Gintaras Praninskas
doaj +3 more sources
A topological based feature extraction method for the stock market
Data Science in Finance and Economics, 2023 We proposed a topology-based method for pre-processed time series data extracted from stock market data. The topology features are extracted from data after denoising and normalization by using a version of weighted Vietoris-Rips complex.
Chen Chang , Hongwei Lin
doaj +1 more source