We show that the Atiyah-Hirzebruch K-theory of spaces admits a canonical generalization for stratified spaces. For this we study algebraic constructions on stratified vector bundles. In particular the tangent bundle of a stratified manifold is such a stratified vector bundle. 1 Families of vector spaces Let R be the field of real numbers and R = R ⊕ · · · ⊕ R be the standard n-dimensional R-vec...

In this paper, we will give a new fixed point theorem for lower semicontinuous multimaps in a Hausdorff topological vector space.

We establish some versions of fixed-point theorem in a Frechet topological vector space E. The main result is that every map A BC where B is a continuous map and C is a continuous linear weakly compact operator from a closed convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has fixed-point. Based on this result, we present two versions of the Kra...

We show that a topology can be defined in the four dimensional space-time of special relativity so as to obtain a topological semigroup for time. The Minkowski 4-vector character of space-time elements as well as the key properties of special relativity are still the same as in the standard theory. However, the new topological structure allows the possibility of an intrinsic asymmetry in the ti...

in this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. so the results in locally convex spaces can be translated in gradual normed linear spaces. finally, we give an examp...

Topological objects of intricate structures have been found in a wide range of systems, like cosmology to liquid crystal1, DNA chains2, superfluid 3He (Ref. 3), quantum Hall magnets4,5, Bose-Einstein condensates6 etc. The topological spin texture in helical magnets, observed in recently7,8, makes a new entry into this fascinating phenomenon. The unusual magnetic behaviour of helimagnet MnSi, no...

We develop further the topological theory of regular variation of [BOst13]. There we established the uniform convergence theorem (UCT) in the setting of topological dynamics (i.e. with a group T acting on a homogenous space X), thereby unifying and extending the multivariate regular variation literature. Here, working with realtime topological ‡ows on homogeneous spaces, we identify an index of...

Kuratowski [6] showed that a continuous compact map f : X → X defined on a closed convex subset X of a Banach space has a fixed point. This theorem has enormous influence on fixed point theory, variational inequalities, and equilibrium problems. In 1968, Goebel [5] established the well-known coincidence theorem, and then there had been a lot of generalization and application (see, [1, 2, 5]). L...