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Proceedings of the National Academy of Sciences, 1935 As a generalization of theorems of L. Pontryagin, E. R. van Kampen and D. van Dantzig, the authors prove the following theorems: Theorem I: A locally compact and separable (not necessarily associative or commutative) field \(F\) is either a hypercomplex system over the real field or is totally disconnected. Theorem III: A locally compact, separable and
Jacobson, Nathan, Taussky, O.
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Locally Compact Hypergroupoids
Indian Journal of Pure and Applied Mathematics, 2020 The authors study locally compact hypergroupoids. Hypergroupoids generalize both hypergroups and groupoids. The authors assume the continuity of the map \((x, y) \mapsto \operatorname{supp}(\delta_{x} \ast \delta_{y})\) and show that the adjoint property in Renault's definition of the left Haar system follows automatically.
Tabatabaie, S. M. +3 more
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Locally compact quantum groups [PDF]
Annales Scientifiques de l’École Normale Supérieure, 2000 Summary: We propose a simple definition of a locally compact quantum group in reduced form. By the word `reduced' we mean that we suppose the Haar weight to be faithful. So in fact we define and study an arbitrary locally compact quantum group, represented on the \(L^2\)-space of its Haar weight.
Kustermans, Johan, Vaes, Stefaan
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Localized Frames and Compactness [PDF]
Journal of Fourier Analysis and Applications, 2015 We introduce the concept of weak-localization for generalized frames and use this concept to define a class of weakly localized operators. This class contains many important operators, including: Short Time Fourier Transform multipliers, Calderon-Toeplitz operators, Toeplitz operators on various functions spaces, Anti-Wick operators, and many others ...
Batayneh, Fawwaz, Mitkovski, Mishko
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Compactness and local compactness in hyperspaces
Topology and its Applications, 2002 In their interesting paper the authors treat compactness and relative compactness of subsets of hyperspaces, where the hyperspaces are considered to be equipped with the Vietoris, the Wijsman and partly the Hausdorff metric topology. Included in the paper are also characterizations of local compactness with respect to the mentioned hyperspace ...
COSTANTINI, Camillo, S. LEVI, J. PELANT
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Locally Compact Contractive Local Groups
, 2009 10 ...
van den Dries, Lou, Goldbring, Isaac
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Journal of Logic and Analysis, 2018 Introduction reorganized and some references ...
Bice, Tristan, Starling, Charles
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Automorphisms of locally compact groups [PDF]
Pacific Journal of Mathematics, 1978 It is proved that for arbitrary locally compact groups G the automorphism group Aut (G) is a complete topological group. Several conditions equivalent to closedness of the group Int (G) of inner automorphisms are given, such as G admits no nontrivial central sequences. It is shown that Aut (G) is topologically embedded in the automorphism group Aut^(G)
Peters, J., Sund, Terje
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Locally Compact Hughes Planes [PDF]
Canadian Mathematical Bulletin, 1994 AbstractAmong the eight-dimensional stable planes, the compact connected generalized Hughes planes and the geometries induced on the outer points are characterized by the property that these planes admit an effective action of the group SL3 ℂ.
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Connecting Locally Compact Abelian Groups [PDF]
Proceedings of the American Mathematical Society, 1983 Those locally compact abelian groups having connected envelopes are characterized as those G G such that the dimension of Hom ( G , R ) {\operatorname {Hom }}(G,R) over R R is finite (where R R is the field of real numbers).
Enochs, Ed, Gerlach, Walt
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