Results 41 to 50 of about 707 (188)
Selections and order-like relations
Applied General Topology, 2001 Every selection f for the family F2(X) of at most two-point subsets of a set X naturally defines an order-like relation on X by if and only . In the present paper we study the relationship between and the possible topologies T on X which realize the ...
Valentin Gutev, Tsugunori Nogura
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All hypertopologies are hit-and-miss
Applied General Topology, 2002 We solve a long standing problem by showing that all known hypertopologies are hit-and-miss. Our solution is not merely of theoretical importance.
Somshekhar Naimpally
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Some properties of hyperspaces of Cech closure spaces with Vietoris-like topologies [PDF]
Filomat, 2010 We study some topological properties of hyperspaces of Cech closure spaces endowed with Vietoris-like topologies. Some of these notions were introduced and considered in [9, 10] and [11], focussing on selection principles.
Andrijević, Dimitrije +2 more
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Some remarks on selectively highly divergent spaces
Applied General TopologyIn this paper, we study selectively highly divergent (SHD) spaces on hyperspaces with the Vietoris topology and the Pixley-Roy topology. Moreover, we show that they are preserved under quasi-perfect countable-to-one mappings and preserved inversely under
Luong Quoc Tuyen +2 more
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Selective Survey on Spaces of Closed Subgroups of Topological Groups
Axioms, 2018 We survey different topologizations of the set S ( G ) of closed subgroups of a topological group G and demonstrate some applications using Topological Groups, Model Theory, Geometric Group Theory, and Topological Dynamics.
Igor V. Protasov
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Scalable Computation of Topological Abstractions for Scalar Data
Computer Graphics Forum, EarlyView.Abstract Topological data analysis has become an important tool for large scale scalar data analysis and visualization, efficiently extracting the inherent structure and features of interest of the data. However, with growing dataset sizes and complexity, it is increasingly becoming infeasible to compute topological abstractions of interest in serial ...
M. Will +6 more
wiley +1 more source
Journal of Scientific Research, 2016 In this article, we define the hyperspace of soft closed sets of a soft topological space (FA, ?). In addition, we define the Vietoris soft topology, ?v, by determining the soft base of this topology which has the form ?FH1, FH2,.....FHn?, where ?FH1, FH2,.....FHn? are soft open sets in (FA, ?).
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Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes [PDF]
Proceedings of the twenty-seventh annual symposium on Computational geometry, 2011 Given a point set that samples a shape, we formulate conditions under which the Rips complex of the point set at some scale reflects the homotopy type of the shape. For this, we associate with each compact set X of R^n two real-valued functions c"X and h"X defined on R"+ which provide two measures of how much the set X fails to be convex at a given ...
Attali, Dominique +2 more
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Topological Graph Neural Networks: A Novel Approach for Geometric Deep Learning
Applied AI Letters, Volume 7, Issue 2, June 2026.This graphical abstract illustrates the Topological Graph Neural Network (TopGNN) architecture. It demonstrates a parallel processing approach where an input graph is simultaneously analyzed by a standard GNN Encoder to capture local node features and by Persistent Homology to extract global topological features (like cycles and voids), visualized as a
Amarjeet +7 more
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The Evolution of Hutchinsonian Climatic Niche Hypervolumes in Gymnosperms
Global Ecology and Biogeography, Volume 35, Issue 6, June 2026.ABSTRACT Aim The niche is a fundamental concept in theoretical and experimental ecology and is used to describe a wide range of ecological processes from species' interactions with the environment to community assemblies. A common way to represent the niche is through a multidimensional geometry known as the Hutchinsonian niche hypervolume.
Fernanda S. Caron +3 more
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