1997  investigated the continuity of the probabilistic norm; they pointed out that each PN space is a topological group but may not be a topological vector space.
n-m] respectively, so H is a topological group homeomorphism.
Thorpe, On summability in topological groups and a theorem of D.
k]alli, On statistical convergence in topological groups, Pure Appl.
Topological Groups: An Introduction provides a self-contained presentation with an emphasis on important families of topological groups.
Filling the need for a broad and accessible introduction to the subject, the book begins with coverage of groups, metric spaces, and topological spaces before introducing topological groups.
Between subcategories of Alexandroff spaces with a group structure categories of finite topological spaces (with a group structure), functional Alexandroff topological spaces (with a group structure), and Alexandroff topological groups has been considered:
Torsion topological groups with minimal open sets, Bulletin of the Australian Mathematical Society, 5(1971), 55-59.
It is well known that there exists a one to one correspondence between Alexandroff topologies on group [member of] which made [member of] a topological group and its normal subgroups (, theorem 4), moreover if for each normal subgroup N of G, [T.
There exists a one to one correspondence between functional Alexandroff topologies on group [member of] which made [member of] a topological group and its finite normal subgroups.
Zhelobenko starts with the basics, including linear algebra and functional analysis, then proceeds to associative algebras, topological groups
, Lie groups, ring theory, and the theory of algebraic groups.