RT - Journal Article
T1 - Homomorphisms on Topological Groups from the Perspective of Bourbaki-boundedness
JF - IJMSI
YR - 2022
JO - IJMSI
VO - 17
IS - 2
UR - http://ijmsi.ir/article-1-1318-en.html
SP - 45
EP - 58
K1 - Topological group
K1 - Bounded set
K1 - Bourbaki-bounded set
K1 - Bourbaki-bounded homomorphism
K1 - Continuous homomorphism
K1 - Compact homomorphism
K1 - Bourbaki-completeness.
AB - In this note we study some topological properties of bounded sets and Bourbaki-bounded sets. Also we introduce two types of Bourbaki-bounded homomorphisms on topological groups including, n$-$Bourbaki-bounded homomorphisms and$hspace{1mm}$ B$-$Bourbaki-bounded homomorphisms. We compare them to each other and with the class of continuous homomorphisms. So, two topologies are presented on them and we determine some properties on domain and range spaces led to Bourbaki-completeness some of these classes of homomorphisms with the given topologies. At the end of this note we focus on n-compact homomorphisms and B-compact homomorphisms briefly.
LA eng
UL http://ijmsi.ir/article-1-1318-en.html
M3 10.52547/ijmsi.17.2.45
ER -