The composition condition arises as a particular case of the center condition for ordinary differential equations. In this paper we describe a topological approach to the composition problem.

in this paper we find sufficient conditions on primitive inverse topological semigroup s under which: the inversion inv : (h(s)) (h(s)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed h-classes is topologically isomorphic to an orthogonal sum p i2= bi (gi) of topological brandt extensions bi (gi) of countably compac...

in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...

Let Γ be an infinite discrete group and βΓ its Čech-Stone compactification. Using the well known fact that a free ultrafilter on an infinite set is nonmeasurable, we show that for each element p of the remainder βΓ \ Γ, left multiplication Lp : βΓ → βΓ is not Borel measurable. Next assume that Γ is abelian. Let D ⊂ l(Γ) denote the subalgebra of distal functions on Γ and let D = Γ = |D| denote t...

The topological charge is constructed for SU(3) center vortex world-surfaces composed of elementary squares on a hypercubic lattice. In distinction to the SU(2) case investigated previously, it is necessary to devise a proper treatment of the color structure at vortex branchings, which arise in the SU(3) case, but not for SU(2). The construction is used to evaluate the topological susceptibilit...