Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.61186/ijmsi
14
8888
13
en
jalali
1401
6
1
gregorian
2022
9
1
17
2
online
1
fulltext
en
Homomorphisms on Topological Groups from the Perspective of Bourbaki-boundedness
عمومى
General
پژوهشي
Research paper
<div style="text-align: justify;">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.</div>
Topological group, Bounded set, Bourbaki-bounded set, Bourbaki-bounded homomorphism, Continuous homomorphism, Compact homomorphism, Bourbaki-completeness.
45
58
http://ijmsi.ir/browse.php?a_code=A-10-3474-1&slc_lang=en&sid=1
M.
Moosaei
moosaeim1987@yahoo.com
`10031947532846009575`

10031947532846009575
No
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
Gh. R.
Rezaei
grezaei@hamoon.usb.ac.ir
`10031947532846009576`

10031947532846009576
No
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
J.
Jamalzadeh
Jamalzadeh1980@math.usb.ac.ir
`10031947532846009577`

10031947532846009577
Yes
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran