in a real separable Hilbert space H driven by an infinite dimensional cylindrical symmetric Lévy process Z = (Zt). The process Z may take values in a Hilbert space 1 Supported by the M.I.U.R. research projects Prin 2004 and 2006 “Kolmogorov equations” and by the Polish Ministry of Science and Education project 1PO 3A 034 29 “Stochastic evolution equations with Lévy noise”. 2 Supported by the Po...

The structure of the Wadge degrees on zero-dimensional spaces is very simple (almost well-ordered), but for many other natural non-zerodimensional spaces (including the space of reals) this structure is much more complicated. We consider weaker notions of reducibility, including the so-called ∆ 0 α-reductions, and try to find for various natural topological spaces X the least ordinal αX such th...

If G is a Polish group, then the category of Polish G-spaces and continuous G-mappings has a universal object. §0. Preface It is known from [2] that 0.1. Theorem (de Vries). Let G be a separable locally compact metric group. Then the category of continuous G-maps and separable complete metric G-spaces has a universal object. In other words, there is a separable complete metric space X on which ...

The study of definable equivalence relations on complete separable metric spaces (i.e., Polish spaces) has emerged as a new direction of research in descriptive set theory over the past twenty years. Quotients of such equivalence relations include the orbit space of an ergodic group action, the set of Turing degrees of subsets of natural numbers, and the space of isomorphism classes of countabl...

Abstract In my paper I would like to analyze two sections of space: natural and cultural landscape (in terms historical geography) their reflection in the toponymic landscape. The greater focus will be on those elements (the shape surface, soil, flora, fauna) (forms types settlements, defense system, administrative divisions borders, economic organization trade, ownership, communication roads),...

Ukrainian Language in Polish Public SpaceThe article deals with examples of the use public space. Ukrainians are largest immigrant group Poland, an estimated 2 million people. Most them speak at elementary level. This situation has led to appearance space Ukrainian-language advertising banks, mobile operators, cinemas, various services, information about COVID-19 pandemic, and so on. Although f...

background & aim : pulse oximetry is a frequently used and standard non-invasive method for monitoring oxygen (o2)-saturation in blood. many factors including dark skin and pigmentation may effect on rate of saturation of the blood oxygen absorbed by pulse oximetry. the effect of nail polish and/or henna color on blood oxygen has not been yet identified and the present study has been carried ou...

We study separable metric spaces with few types of countable dense sets. We present a structure theorem for locally compact spaces having precisely n types of countable dense sets: such a space contains a subset S of size at most n−1 such that S is invariant under all homeomorphisms of X and X \ S is countable dense homogeneous. We prove that every Borel space having fewer than c types of count...