A few remarks on boundedness in topological modules and topological groups

Let $X$, $Y$, and $Z$ be topological modules over a topological ring $R$. In the first part of the paper, we introduce three different classes of bounded bigroup homomorphisms from $X\times Y$ into $Z$ with respect to the three different uniform convergence topologies. We show that these spaces form again topological modules over $R$. In the second part, we characterize bounded sets in the arbitrary product of topological groups with respect to the both product and box topologies.

Keywords:

Bigroup homomorphism, topological module, boundedness topological group,

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V. Arnautov, S. Glavatsky and A.A. Mikhalev, Introduction to the theory of topological rings and modules, Pure and Applied Mathematics, CRC press, 1995.
T. Husain, Introduction to topological groups, W. B. Saunders Company, 1966.
Lj.D.R. Kocinac and O. Zabeti, Topological groups of bounded homomorphisms on a topological group, Filomat, 30 (3), 541–546, 2016.
M. Mirzavaziri and O. Zabeti, Topological rings of bounded and compact group homo- morphisms on a topological ring, J. Adv. Res. Pure Math. 3 (2), 100–106, 2011.
N. Shell, Topological fields and near valuations, Marcel Dekker, Inc. The city univer- sity of New York, New York, 1990.
V.G. Troitsky, Spectral radii of bounded linear operators on topological vector spaces, Panamer. Math. J. 11 (3), 1–35, 2001.
O. Zabeti, Topological algebras of bounded operators on topological vector spaces, J. Adv. Res. Pure Math. 3 (1), 22–26, 2011.
O. Zabeti and Lj.D.R. Kocinac, A few remarks on bounded operators on topological vector spaces, Filomat, 30 (3), 763–772, 2016.

Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

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