This paper is devoted to the completeness issue of RMLCI | the relative modal logic with composition and intersection | a restriction of the propositional dynamic logic with intersection. The trouble with RMLCI is that the operation of intersection is not modally deenable. Using the notion of mosaics, we give a new proof of a theorem considered in a previous paper \Complete axiomatization of a ...

Let $(*) denote the family of subsets of the unit square defined to be of first category (Lebesgue measure zero) in almost every vertical line in the sense of measure (category). Theorem 1. There is a homeomorphism of the unit square onto itself mapping a given set in tyji?) onto a set of Lebesgue measure zero. Theorem 2. There is a set belonging to both Í» and * that cannot be mapped onto a se...

We show that the space of all Lelek fans in a Cantor fan, equipped with the Hausdorff metric, is homeomorphic to the separable Hilbert space. This result is a special case of a general theorem we prove about spaces of upper semicontinuous functions on compact metric spaces that are strongly discontinuous.

First, we answer a question of Pestov, by proving that the full group of a sofic equivalence relation is a sofic group. Then, we give a short proof of the theorem of Grigorchuk and Medynets that the topological full group of a minimal Cantor homeomorphism is LEF. Finally, we show that for certain non-amenable groups all the generalized lamplighter groups are sofic.

A vanishing theorem is proved for`-adic cohomology with compact support on a singular aane complete intersection. As an application, it is shown that for an aane complete intersection deened over a nite eld of q elements, the reciprocal \poles" of the zeta function are always divisible by q as algebraic integers. A p-adic proof is also given, which leads to further q-divisibility of the poles o...

In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...

We prove a theorem whose countable version is that a zero-dimensional polyadic space of countable tightness is a Uniform Eberlein compact space. We prove that if a point p of a polyadic space Y has πχ(p, Y ) = κ > ω, then there exists K ⊂ Y such that p ∈ K and K is homeomorphic to the Cantor cube 2.

We construct, for any " good " Cantor set F of S n−1 , an immersion of the sphere S n with set of points of zero Gauss-Kronecker curvature equal to F ×D 1 , where D 1 is the 1-dimensional disk. In particular these examples show that the theorem of Matheus-Oliveira strictly extends two results by do Carmo-Elbert and Barbosa-Fukuoka-Mercuri.

A theorem of Picard type is proved for entire holomorphic mappings into projective varieties. This theorem has local nature in the sense that the existence of Julia directions can be proved under natural additional assumptions. An example is given which shows that Borel’s theorem on holomorphic curves omitting hyperplanes has no such local counterpart. Let P be complex projective space of dimen...