Results 71 to 80 of about 2,822 (176)
A short note on hit-and-miss hyperspaces
Applied General Topology, 2003 Based on some set-theoretical observations, compactness results are given for general hit-and-miss hyperspaces. Compactness here is sometimes viewed splitting into “κ-Lindelöfness” and “κ-compactness” for cardinals κ.
René Bartsch, Harry Poppe
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A Validation Methodology for XAI Decision Support Systems Against Relational Domain Properties
Journal of Software: Evolution and Process, Volume 37, Issue 10, October 2025.ABSTRACT The global adoption of artificial intelligence (AI) has increased dramatically in recent years, becoming commonplace in many fields. Such a pervasiveness has led to changes in how AI is perceived, strengthening discussions on its societal consequences. Thus, a new class of requirements for AI‐based solutions emerged. Broadly speaking, those on
Emanuele De Angelis +3 more
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Acta Crystallographica Section C, Volume 81, Issue 10, Page 559-569, October 2025.A step‐by‐step outline for academic and industrial practitioners determining molecular organic crystal structures from powder X‐ray diffraction data.This article focuses on a specific real‐space methodology for solving and refining molecular organic crystal structures, developed by the authors and collaborators.
Elena Kabova +4 more
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Extension of Hyperspace Selections
, 2023 In 1951, Ernest Michael wrote a definitive seminal article on hyperspaces raising a general question that became known as the hyperspace selection problem. The present paper contains some aspects of this problem, along with several open questions. Most of these considerations and questions are related to the usual map extension problem, but now in the ...
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Mitochondrial Dysfunction in Neurodegenerative Diseases
MedComm, Volume 6, Issue 9, September 2025.Overview of mitochondrial dysfunction in neurodegenerative diseases (NDDs). Mitochondrial dysfunction in NDDs involves impaired ATP synthesis, Ca2+ imbalance, oxidative stress, and apoptosis. Assessment methods integrate functional assays, omics, and imaging.
Chongyang Chen +10 more
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Approximating Fixed Points of Nonexpansive Mappings in Hyperspaces
Fixed Point Theory and Applications, 2007 Two convergence theorems for the Ishikawa and Mann iteration sequences involving nonexpansive mappings in hyperspaces are established.
Feng Chi +3 more
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Semi separation axioms and hyperspaces
International Journal of Mathematics and Mathematical Sciences, 1981 In this paper examples are given to show that s-regular and s-normal are independent; that s-normal, and s-regular are not semi topological properties; and that (S(X),E(X)) need not be semi-T1 even if (X,T) is compact, s-normal, s-regular, semi-T2, and ...
Charles Dorsett
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Some problems on selections for hyperspace topologies
Applied General Topology, 2004 The theory of hyperspaces has attracted the attention of many mathematicians who have found a large variety of its applications during the last decades.
Valentin Gutev, Tsugunori Nogura
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On hyperspaces of polyhedra [PDF]
Proceedings of the American Mathematical Society, 1990 Let Q = [ − 1 , 1 ] ω Q = {[ - 1,1]^\omega } be the Hilbert cube and \[ Q f = { ( x
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Local Connectedness in Hyperspaces
Rocky Mountain Journal of Mathematics, 2006 \textit{W. Makuchowski} [Bull. Pol. Acad. Sci., Math. 47, No. 2, 119--126 (1999; Zbl 0929.54012)] has proved that if \(X\) is a Hausdorff compact space, then local connectedness and local arcwise connectedness of the hyperspace \(C(X)\) of all subcontinua of \(X\) and of the hyperspace \(2^X\) of all non-empty closed subsets of \(X\) are equivalent at ...
Charatonik, Janusz J. +1 more
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