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 ?
Granirer, On invariant mean on topological semigroups and on topological groups Pacific J.
If we set S := G x T, where G is an abelian topological group, then S is a reflexive foundation semigroup and again by Theorem 4.
Keywords: Semi open set, semi closed set, irresolute mapping, semi homeomorphism, irresolute topological group, semi connected space, semi component, semi topological groups with respect to irresoluteness.
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.
Thorpe, On summability in topological groups and a theorem of D.
Topological Groups: An Introduction provides a self-contained presentation with an emphasis on important families of topological groups.
Motivated by results of [1] and [2], we introduce in this note another notion of "independence" between representations of a topological group and prove that under some suitable conditions, representations of the absolute Galois group of a number field associated with two elliptic curves are "independent" in this sense.
Similar results are obtained in [1] for (symmetric) continuous cohomology of topological groups, denoted (H[S.
They cover Lebesgue measure in Euclidean space, measures on metric spaces, topological groups, Banach and measure, compact groups have a Haar measure, applications, Haar measure on locally compact groups, metric invariance and Haar measure, Steinlage on Haar measure, and Oxtoby's view of Haar measure.
A theorem on functional Alexandroff topological groups.
The 64 papers in this collection explore field theory and polynomials, commutative rings and algebras, matrix theory, associative rings, K-theory, group theory and generalizations, topological groups, Lie groups, and differential geometry.