In this paper we give some characterizations of topological extreme amenability. Also we answer a question raised by Ling [5]. In particular we prove that if T is a Borel subset of a locally compact semigroup S such that M(S)* has a multiplicative topological left invariant mean then T is topological left lumpy if and only if there is a multiplicative topological left invariant mean M on M(S)* ...

In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.

Abstract. In this paper, we first derive specific results concerning the continuity and upper semi-continuity of the spectral radius and spectrum functions on fundamental locally multiplicative topological algebras. We continue our investigation by further determining the automatic continuity of linear mappings and homomorphisms in these algebras.

we define a new function-valued inner product on l2(g), called ?-bracket product, where g is a locally compact abelian group and ? is a topological isomorphism on g. we investigate the notion of ?-orthogonality, bessel's inequality and ?-orthonormal bases with respect to this inner product on l2(g).

let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...