We report transport studies on magnetically doped Bi(2)Se(3) topological insulator ultrathin films grown by molecular beam epitaxy. The magnetotransport behavior exhibits a systematic crossover between weak antilocalization and weak localization with the change of magnetic impurity concentration, temperature, and magnetic field. We show that the localization property is closely related to the m...

The recent experimental realization of a the quantum spin hall e ect has caused a lot of interest in these topological states of matter. Topological insulators are a new form of condensed matter that are not characterized by a spontaneously broken symmetry. Instead the materials are characterized by topology of the manifold of the occupied bloch states. Topological insulators have the unique pr...

In this paper we prove the following theorem. “Let H be a countably Čech–complete topological group, X be a topological space and (G, ·, τ) be a topological group. If f : H ×X → G is a separately continuous mapping with the property that for each x ∈ X, the mapping h 7→ f(h, x) is a group homomorphism, then for each q–point x0 ∈ X the mapping f is jointly continuous at each point of H ×{x0}.” W...

(A) We study in this paper some connections between the Fra¨ıssé theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures. A prime concern of topological dynamics is the study of continuous actions of (Haus-dorff) topological groups G on (Hausdorff) compact spaces X. These are usually referred to as (c...

A simple topological graph is a graph drawn in the plane so that its edges are represented by continuous arcs with the property that any two of them meet at most once. Using a new tool developed in [12] we show that every simple topological graph on n vertices contains Ω(n 1 2 / √ log n) pairwise disjoint edges. This improves the previous lower bound of Ω(n 1 3 ) by Suk [17] and by Fulek and Ru...

Mathematical descriptors of molecular structure, such as various topological indices, have been widely used in structure-property-activity studies (see [5, 6, 12]). Among the numerous topological indices considered in chemical graph theory, only a few have been found noteworthy in practical application (see [10]). One of these is the connectivity index or Randić index. The Randić index of an or...

In this paper we characterize various sorts of boundedness of the free (abelian) topological group F (X) (A(X)) as well as the free locally-convex linear topological space L(X) in terms of properties of a Tychonoff space X. These properties appear to be close to so-called selection principles, which permits us to show, that (it is consistent with ZFC that) the property of Hurewicz (Menger) is l...

We investigate powerspace constructions on topological spaces, with a particular focus on the category of quasi-Polish spaces. We show that the upper and lower powerspaces commute on all quasi-Polish spaces, and show more generally that this commutativity is equivalent to the topological property of consonance. We then investigate powerspace constructions on the open set lattices of quasi-Polis...

(A) We study in this paper some connections between the Fra¨ıssé theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures. A prime concern of topological dynamics is the study of continuous actions of (Haus-dorff) topological groups G on (Hausdorff) compact spaces X. These are usually referred to as (c...

(A) We study in this paper some connections between the Fra¨ıssé theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures. A prime concern of topological dynamics is the study of continuous actions of (Haus-dorff) topological groups G on (Hausdorff) compact spaces X. These are usually referred to as (c...