In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

We define united K-theory for real C*-algebras, generalizing Bousfield’s topological united K-theory. United K-theory incorporates three functors — real K-theory, complex K-theory, and self-conjugate K-theory — and the natural transformations among them. The advantage of united K-theory over ordinary K-theory lies in its homological algebraic properties, which allow us to construct a Künneth-ty...

Let Var be the category of complex algebraic varieties, Top that of nice topological spaces, Dab be the derived category of finite complexes of finitely generated abelian groups. One has tensor functors Var → Top → Dab, the first assigns to a variety its space equipped with the classical topology, the second one is the singular chain complex functor (the tensor structure for the first two categ...

The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front set satisfies some conditions. Thus, it is natural to investigate the topological properties of these operations between spaces D′ Γ of distributions having a wave front set included in a given closed cone Γ of the cotangent space. As discovered by S. Alesker, the pull-back is...

We study the transport properties of pinned striped quantum Hall phases. We show that, under quite general assumptions, the macroscopic conductivity tensor satisfies a semicircle law. In particular, this result is valid for both smectic and nematic stripe phases, independent of the presence of topological and orientational defects such as dislocations and grain boundaries. As a special case, ou...

Let Var be the category of complex algebraic varieties, Top that of nice topological spaces, Dab be the derived category of finite complexes of finitely generated abelian groups. One has tensor functors Var → Top → Dab, the first assigns to a variety its space equipped with the classical topology, the second one is the singular chain complex functor (the tensor structure for the first two categ...

This paper is concerned with the algebraic K-theory of locally convex C-algebras stabilized by operator ideals, and its comparison with topological K-theory. We show that if L is locally convex and J a Fréchet operator ideal, then all the different variants of topological K-theory agree on the completed projective tensor product L⊗̂J , and that the obstruction for the comparison map K(L⊗̂J ) → K(...

One shows that for two C-algebras A1 and A2 any continuous function on Prim(A1)×Prim(A2) can be continuously extended to Prim(A1⊗min A2) provided it takes its values in a T1 topological space. This generalizes [5, Corollary 3.4]. A new proof is given for a result of Archbold [2] about the space of minimal primal ideals of A1 ⊗min A2. To obtain these two results one makes use of the topological ...

We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...