S OF SHORT COMMUNICATIONS AND POSTERS Alonso González, Clementa Title: Topological invariants of singularities of real vector fields in dimension three. Abstract: We give topological invariants for a wide class H(π) of absolutely isolated singularities of three-dimensional vector fields. Our invariants are complete once the desingularization morphism π is fixed. They are obtained in terms of a ...

Sunada’s work on topological crystallography emphasizes the role of the ‘maximal abelian cover’ of a graph X. This is a covering space of X for which the group of deck transformations is the first homology group H1(X,Z). An embedding of the maximal abelian cover in a vector space can serve as the pattern for a crystal: atoms are located at the vertices, while bonds lie on the edges. We prove th...

For a new class of topological vector spaces, namely κ-normed spaces, an associated quasisemilinear topological preordered space is defined and investigated. This structure arise naturally from the consideration of a κ-norm, that is a distance function between a point and a G δ-subset. For it, analogs of the Hahn-Banach theorem are proved.

Existence of zeros for operators taking their values in the dual of a Banach space BIAGIO RICCERI Throughout the sequel, E denotes a reflexive real Banach space and E * its topological dual. We also assume that E is locally uniformly convex. This means that for each x ∈ E, with x = 1, and each ǫ > 0 there exists δ > 0 such that, for every y ∈ E satisfying y = 1 and x − y ≥ ǫ, one has x + y ≤ 2(...

on a hypergroupoid one can define a topology such that the hyperoperationis pseudocontinuous or continuous. in this paper we extend thisconcepts to the fuzzy case. we give a connection between the classical and thefuzzy (pseudo)continuous hyperoperations.

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

It is known that many integrable systems can be reduced from self-dual Yang-Mills equations. The formal solution space to the self-dual Yang-Mills equations is given by the so called ADHM construction, in which the solution space are graded by vector spaces with dimensionality concerning topological index. When we consider a reduced self-dual system such as the Bogomol’nyi equations, in terms o...

In this paper, by using C-sequentially sign property for bifunctions, we provide sufficient conditions that ensure the existence of solutions of some vector equilibrium problems in Hausdorff topological vector spaces which ordered by a cone. The conditions which we consider are not imposed on the whole domain of the operators involved, but just on a locally segment-dense subset of the domain.

We describe the structure of 0-simple countably compact topological inverse semigroups and the structure of congruence-free countably compact topological inverse semigroups. We follow the terminology of [3, 4, 8]. In this paper all topological spaces are Hausdorff. If S is a semigroup then we denote the subset of idempotents of S by E(S). A topological space S that is algebraically a semigroup ...