Quasi-essential subsocles of Abelian p-groups
Moore, J. Douglas (1979)
Portugaliae mathematica
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Moore, J. Douglas (1979)
Portugaliae mathematica
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Siap, Irfan, Kulhan, Nilgun (2005)
Applied Mathematics E-Notes [electronic only]
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Félix Cabello Sánchez (2003)
Fundamenta Mathematicae
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We study the stability of homomorphisms between topological (abelian) groups. Inspired by the "singular" case in the stability of Cauchy's equation and the technique of quasi-linear maps we introduce quasi-homomorphisms between topological groups, that is, maps ω: 𝒢 → ℋ such that ω(0) = 0 and ω(x+y) - ω(x) - ω(y) → 0 (in ℋ) as x,y → 0 in 𝒢. The basic question here is whether ω is approximable by a true homomorphism a in the sense that ω(x)-a(x) → 0...
F. Catanese, F. Capocasa (1995)
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Robert H. Lohman (1974)
Colloquium Mathematicae
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Ch. Megibben (1969)
Bulletin de la Société Mathématique de France
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Pablo F. Meilán, Mariano Creus, Mario Garavaglia (2000)
Visual Mathematics
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Cabiria Andreian Cazacu (1981)
Annales Polonici Mathematici
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T. K. Pal, M. Maiti (1977)
Matematički Vesnik
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Roman Sikorski (1974)
Fundamenta Mathematicae
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D. J. Grubb (2008)
Fundamenta Mathematicae
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A quasi-linear map from a continuous function space C(X) is one which is linear on each singly generated subalgebra. We show that the collection of quasi-linear functionals has a Banach space pre-dual with a natural order. We then investigate quasi-linear maps between two continuous function spaces, classifying them in terms of generalized image transformations.