topological group

(redirected from Topological groups)
Also found in: Encyclopedia.

topological group

n
maths a group, such as the set of all real numbers, that constitutes a topological space and in which multiplication and inversion are continuous
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
Mentioned in ?
References in periodicals archive ?
Periodic Locally Compact Groups: A Study of a Class of Totally Disconnected Topological Groups
We expect, this paper will promote the future study on neutrosophic soft topological groups and many other general frameworks.
Markoff, "On free topological groups," Doklady Akademii Nauk SSSR, vol.
A renowned Turk academic figure, Dr Ekrem Savas, presented his research article on 'Lacunary Double Statistical Convergence of order in Topological Groups'.
Granirer, On invariant mean on topological semigroups and on topological groups Pacific J.
This class of semigroups is very extensive for which discrete semigroups and topological groups are elementary examples.
In this paper, we will continue the study of irresolute topological groups. We will investigate semi connectedness for irresolute topological groups.
In this paper, we introduce and study the concepts of statistical convergence, strongly convergence, lacunary statistical convergence and lacunary strongly convergence for interval numbers in topological groups as follows.
The Euclidean space R and the PN space (V, v, [tau], [[tau].sup.*]) are two topological groups. For a fixed vector p [member of] V, the scalar multiplication f : R [right arrow] (V, v, [tau], [[tau].sup.*]) that is defined by f(a) = ap is continuous iff f is continuous at 0.
The purpose of this article is to give certain characterizations of I-convergent sequences in topological groups and to obtain extensions of a decomposition theorem and a completeness theorem to topological groups.
Among his topics are topological groups, left invariant topologies and strongly discrete filters, ultrafilter semigroups, almost maximal topological groups, and resolvability.
Among the topics are commutative topological groups, locally convex spaces and semi-norms, Hahn-Banach theorems, barreled spaces, closed graph theorems, and reflexivity.