Abstract

Let $X$ be a topological ring. In this paper, we consider the three classes ($btb$-bounded, $tbtb$-bounded, and $tbb$-bounded) of endomorphisms defined on $X$ and denote these classes by $B_{btb}(X), B_{tbtb}(X)$, and $B_{tbb}(X)$, respectively. We equip them with an appropriate topology and we find some sufficient conditions under which, each class of these endomorphisms is complete.

Keywords: Totally bounded endomorphism; completeness; topological ring.

MSC: 54H13, 16W80

Pages:  419$-$424     

Volume  65 ,  Issue  3 ,  2013