TY - JOUR
JF - IJMSI
JO - IJMSI
VL - 17
IS - 2
PY - 2022
Y1 - 2022/9/01
TI - Homomorphisms on Topological Groups from the Perspective of Bourbaki-boundedness
TT -
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.
SP - 45
EP - 58
AU - Moosaei, M.
AU - Rezaei, Gh. R.
AU - Jamalzadeh, J.
AD - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
KW - Topological group
KW - Bounded set
KW - Bourbaki-bounded set
KW - Bourbaki-bounded homomorphism
KW - Continuous homomorphism
KW - Compact homomorphism
KW - Bourbaki-completeness.
UR - http://ijmsi.ir/article-1-1318-en.html
DO - 10.52547/ijmsi.17.2.45
ER -