TY - JOUR
T1 - Homomorphisms on Topological Groups from the Perspective of Bourbaki-boundedness
TT -
JF - IJMSI
JO - IJMSI
VL - 17
IS - 2
UR - http://ijmsi.ir/article-1-1318-en.html
Y1 - 2022
SP - 45
EP - 58
KW - Topological group
KW - Bounded set
KW - Bourbaki-bounded set
KW - Bourbaki-bounded homomorphism
KW - Continuous homomorphism
KW - Compact homomorphism
KW - Bourbaki-completeness.
N2 - 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.
M3 10.52547/ijmsi.17.2.45
ER -