Results 21 to 30 of about 212 (106)
Concerning connected, pseudocompact Abelian groups
Topology and its Applications, 1989 To avoid repetition, all groups in the sequel are assumed to be completely regular topological abelian groups. It is known [\textit{W. W. Comfort} and \textit{T. Soundararajan}, Pac. J. Math. 100, 61-84 (1982; Zbl 0451.22002)] that for every infinite cardinal \(\alpha\), there is an \(\omega\)-bounded (i.e., every countable subset has compact closure ...
Comfort, W.W., van Mill, Jan
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Weakly pseudocompact subsets of nuclear groups
Journal of Pure and Applied Algebra, 1999 \textit{W. Banaszczyk} introduced in [Additive subgroups of topological vector spaces, Lect. Notes Math., vol. 1466 (Berlin etc. 1991; Zbl 0743.46002)] the class of nuclear groups. This class contains every locally compact Abelian (LCA) group and the additive groups of all nuclear locally convex spaces.
Banaszczyk, W., Martín-Peinador, E.
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On the quasi-component of pseudocompact abelian groups
Topology and its Applications, 2012 In this paper, we describe the relationship between the quasi-component q(G) of a (perfectly) minimal pseudocompact abelian group G and the quasi-component q(\widetilde G) of its completion. Specifically, we characterize the pairs (C,A) of compact connected abelian groups C and subgroups A such that A \cong q(G) and C \cong q(\widetilde G).
Dikranjan, D., Lukács, Gábor
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The dual of a pseudocompact group refining the topology of the circle group
Topology and its Applications, 2012 The author presents an example of a reflexive (reflexivity in the sense of Pontryagin-van Kampen's duality theory), pseudocompact, non-compact, monothetic group \(H\) such that the Pontryagin dual \(H^\wedge\) of \(H\) is precompact, connected, Baire, and admits a continuous isomorphism onto the circle group.
Tkachenko, Mikhail
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Chains of pseudocompact group topologies
Journal of Pure and Applied Algebra, 1998 For an infinite cardinal \(\sigma\) and a group \(G\) let \({\mathcal P}_\sigma (G)\) be the poset of all pseudocompact group topologies of weight \(\sigma\) on \(G\). \({\mathcal P} (\sigma)\) denotes the class of groups admitting a pseudocompact group topology of weight \(\sigma\), and let \({\mathbf P} (\sigma)\) be the power set of \(\sigma\). Then
DIKRANJAN, Dikran
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C-compact and r-pseudocompact subsets of paratopological groups
Topology and its Applications, 2016 It is known that the concepts of \(C\)-compactness and \(r\)-pseudocompactness coincide in topological groups. In this paper the authors determine several classes of Tychonoff paratopological groups in which \(C\)-compact and \(r\)-pseudocompact subsets coincide (these include totally \(\omega\)-narrow paratopological groups, commutative ...
Sánchez, Iván, Tkachenko, Mikhail G.
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Differential graded Koszul duality: An introductory survey
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1551-1640, August 2023., 2023 Abstract This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir L. Positselski, Memoirs of the American Math. Society 212 (2011), no. 996, vi+133. The paper is intended to serve as a pedagogical introduction and a summary of the covariant duality between DG‐algebras and curved DG‐coalgebras, as ...
Leonid Positselski
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[Retracted] Double Weak Hopf Quiver and Its Path Coalgebra
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 The main input of this research is the introduction of the concept of double weak Hopf quiver (DWHQ). In addition, the structures of weak Hopf algebra (WHA) are obtained through path coalgebra of the proposed quivers. Furthermore, the module and comodule structures on the said WHA are discussed.
Muhammad Naseer Khan +6 more
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Weak Hopf Algebra and Its Quiver Representation
Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021 This study induced a weak Hopf algebra from the path coalgebra of a weak Hopf quiver. Moreover, it gave a quiver representation of the said algebra which gives rise to the various structures of the so‐called weak Hopf algebra through the quiver. Furthermore, it also showed the canonical representation for each weak Hopf quiver.
Muhammad Naseer Khan +5 more
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A pseudocompact group which is not strongly pseudocompact
Topology and its Applications, 2015 A topological space \(X\) is \textit{strongly pseudocompact} if for every sequence \((U_n)_{n\in\mathbb N}\) of pairwise disjoint non-empty open subsets of \(X\) there exists a sequence \((x_n)_{n\in\mathbb N}\) in \(X\) such that \(x_n\in U_n\) for every \(n\in\mathbb N\) and \(cl_X(\{x_n : n \in\mathbb N\})\setminus\left( \bigcup_{n\in\mathbb N}U_n ...
Garcia-Ferreira, S., Tomita, A. H.
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