Title : ( Topological rings of bounded and compact group homomorphisms on a topological ring )
Authors: Madjid Mirzavaziri , omid zabeti ,
Full TextAbstract
Let X be a topological ring. In this paper, we consider the three classes of nr-bounded, br-bounded and cr-continuous group homomorphisms defined on X and denote these classes by Bnr(X);Bbr(X) and Bcr(X), respectively. We show that the operations of addition and product in Bnr(X);Bbr(X) and Bcr(X) are continuous with respect to the topology considered on them. Moreover, we introduce the classes of nr-compact and br-compact group homomorphisms, and we study the situations where a class of bounded group homomorphisms coincides with the corresponding class of compact group homomorphisms.
Keywords
Bounded group homomorphism; Continuous group homomorphism; Compact group homomorphism; Topological ring.
@article{paperid:1022066,
author = {Madjid Mirzavaziri, and Zabeti, Omid},
title = {Topological rings of bounded and compact group homomorphisms on a topological ring},
journal = {Journal of Advanced Research in Pure Mathematics},
year = {2011},
volume = {3},
number = {2},
month = {March},
issn = {1943-2380},
pages = {100--106},
numpages = {6},
keywords = {Bounded group homomorphism; Continuous group homomorphism; Compact group
homomorphism; Topological ring.},
}
%0 Journal Article
%T Topological rings of bounded and compact group homomorphisms on a topological ring
%A Madjid Mirzavaziri,
%A Zabeti, Omid
%J Journal of Advanced Research in Pure Mathematics
%@ 1943-2380
%D 2011
