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 [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.

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 in [1].

* 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.