Graev, "Free topological groups
," Izvestiya Akademii Nauk SSSR Seriya Matematicheskaya, vol.
When S is a topological group
, then LUC(S) is the set of all uniformly continuous functions on S with respect to the right uniformity of S i.e., f [member of] LUC(S) [??] [for all] [epsilon] > 0, [there exists] U neighborhood of the identity of S such that [s.sup.-1]t [member of] U [??] [absolute value of f (s) - f (t)] [less than or equal to] [epsilon].
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 4.1, [M.sub.a](S) is BSE.
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.
Lacunary statistical convergence in topological groups
. Indian Journal of Pure and Applied Mathematics, v.
In studying the strong topologies on the generalized PN spaces, Alsina et al., 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.
Among the topics are functional algebras of operators generated by a self-adjoint operator in Pontryagin space ?1, Wedderburn structure theorems for two-sided locally m-convex H*-algebras, main embedding theorems for symmetric spaces of measurable functions, discrete non-closed subsets in maximally non-discrete topological groups
, faithfully representable topological *-algebras: some spectral properties, and dense ideals in topological algebras: some results and open problems.
By definition of [bar.[??]], we have the following commutative diagram of (compact) topological groups
with exact rows
As it has been done for topological groups
; we wish to introduce a topol- ogy on hypergroup in such a way that the hyperoperation becomes continue.
Singh also studies symmetric continuous cohomology of topological groups
* 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.