Filomat 2016 Volume 30, Issue 3, Pages: 541-546
https://doi.org/10.2298/FIL1603541K
Full text ( 236 KB)
Topological groups of bounded homomorphisms on a topological group
Kočinac Ljubiša (Faculty of Sciences and Mathematics, Niš)
Zabeti Omid (University of Sistan and Baluchestan, Faculty of Mathematics, Zahedan, Iran)
We consider a few types of bounded homomorphisms on a topological group.
These classes of bounded homomorphisms are, in a sense, weaker than the class
of continuous homomorphisms. We show that with appropriate topologies each
class of these homomorphisms on a complete topological group forms a complete
topological group.
Keywords: bounded homomorphism, continuous homomorphism, topological group, completeness