this paper gives a short survey of some of the known results generalizing the theorem, credited to i. schur, that if the central factor group is finite then the derived subgroup is also finite.

We introduce the notion of a matrad M = {Mn,m} whose submodules M∗,1 and M1,∗ are non-Σ operads. We construct a functor from PROP to matrads and its inverse, the universal enveloping functor. We define the free matrad H∞, generated by a singleton in each bidegree (m, n) 6= (1, 1), and define an A∞-bialgebra as an algebra over H∞. We realize H∞ as the cellular chains of polytopes {KKn,m = KKm,n}...

In this paper, we study the existence of solutions for vector saddle points problems in a general setting. Our approach, first, is based on the KKM lemma and a relaxation of the C− lower semicontinuity notion introduced by T.Tanaka by means of an extension to the vector setting of a Bŕezis-NirenbergStampacchia condition, and arguments from generalized convexity. This leads us to generalize and ...

We establish the existence of a best proximity pair for which the best proximity set is nonempty for a finite family of multimaps whose product is either an Ac -multimap or a multimap T : A → 2 such that both T and S ◦ T are closed and have the KKM property for each Kakutani multimap S : B → 2. As applications, we obtain existence theorems of equilibrium pairs for free n-person games as well as...

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.