topological groups


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topological groups

[¦täp·ə¦läj·ə·kəl ′grüps]
(mathematics)
Groups which also have a topology with the property that the group operation and the inverse operation determine continuous functions.
References in periodicals archive ?
1997 [3] 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 ([4], 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.