scholarly journals A Q‐WADGE HIERARCHY IN QUASI‐POLISH SPACES

2020 ◽  
pp. 1-27
Author(s):  
VICTOR SELIVANOV
Keyword(s):  
Polish Spaces ◽  
Wadge Hierarchy

scholarly journals Wadge-like reducibilities on arbitrary quasi-Polish spaces

2014 ◽  
Vol 25 (8) ◽  
pp. 1705-1754 ◽  
Author(s):  
LUCA MOTTO ROS ◽  
PHILIPP SCHLICHT ◽  
VICTOR SELIVANOV
Keyword(s):  
Real Line ◽  
Polish Space ◽  
Baire Space ◽  
Topological Spaces ◽  
Polish Spaces ◽  
The Real ◽  
Degree Structure ◽  
Wadge Hierarchy

The structure of the Wadge degrees on zero-dimensional spaces is very simple (almost well ordered), but for many other natural nonzero-dimensional spaces (including the space of reals) this structure is much more complicated. We consider weaker notions of reducibility, including the so-called Δ0α-reductions, and try to find for various natural topological spaces X the least ordinal αX such that for every αX ⩽ β < ω1 the degree-structure induced on X by the Δ0β-reductions is simple (i.e. similar to the Wadge hierarchy on the Baire space). We show that αX ⩽ ω for every quasi-Polish space X, that αX ⩽ 3 for quasi-Polish spaces of dimension ≠ ∞, and that this last bound is in fact optimal for many (quasi-)Polish spaces, including the real line and its powers.

scholarly journals Some Random Coupled Best Proximity Points for a Generalized ω-Cyclic Contraction in Polish Spaces

2017 ◽  
Vol 59 (1) ◽  
pp. 91-105 ◽  
Author(s):  
C. Kongban ◽  
P. Kumam
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Cyclic Contraction ◽  
Polish Spaces ◽  
Best Proximity Points ◽  
Coupled Best Proximity Point

AbstractIn this paper, we will introduce the concepts of a random coupled best proximity point and then we prove the existence of random coupled best proximity points in separable metric spaces. Our results extend the previous work of Akbar et al.[1].

scholarly journals Graph directed Markov systems on Hilbert spaces

2009 ◽  
Vol 147 (2) ◽  
pp. 455-488 ◽  
Author(s):  
R. D. MAULDIN ◽  
T. SZAREK ◽  
M. URBAŃSKI
Keyword(s):  
Hausdorff Measure ◽  
Iterated Function System ◽  
Sufficient Conditions ◽  
Topological Pressure ◽  
Limit Set ◽  
Covering Theorem ◽  
Limit Sets ◽  
Markov Systems ◽  
Polish Spaces ◽  
Iterated Function

AbstractWe deal with contracting finite and countably infinite iterated function systems acting on Polish spaces, and we introduce conformal Graph Directed Markov Systems on Polish spaces. Sufficient conditions are provided for the closure of limit sets to be compact, connected, or locally connected. Conformal measures, topological pressure, and Bowen's formula (determining the Hausdorff dimension of limit sets in dynamical terms) are introduced and established. We show that, unlike the Euclidean case, the Hausdorff measure of the limit set of a finite iterated function system may vanish. Investigating this issue in greater detail, we introduce the concept of geometrically perfect measures and provide sufficient conditions for geometric perfectness. Geometrical perfectness guarantees the Hausdorff measure of the limit set to be positive. As a by–product of the mainstream of our investigations we prove a 4r–covering theorem for all metric spaces. It enables us to establish appropriate co–Frostman type theorems.

scholarly journals Duality Theorem for a Minimax Vector Optimization Problem

2021 ◽  
Author(s):  
Jacob Atticus Armstrong Goodall
Keyword(s):  
Vector Optimization ◽  
Duality Theorem ◽  
Optimization Problem ◽  
Optimal Transport ◽  
Probability Distributions ◽  
Vector Optimization Problem ◽  
Complexity Science ◽  
Polish Spaces ◽  
Leibler Divergence ◽  
Mathematical Optimisation

Abstract A duality theorem is stated and proved for a minimax vector optimization problem where the vectors are elements of the set of products of compact Polish spaces. A special case of this theorem is derived to show that two metrics on the space of probability distributions on countable products of Polish spaces are identical. The appendix includes a proof that, under the appropriate conditions, the function studied in the optimisation problem is indeed a metric. The optimisation problem is comparable to multi-commodity optimal transport where there is dependence between commodities. This paper builds on the work of R.S. MacKay who introduced the metrics in the context of complexity science in [4] and [5]. The metrics have the advantage of measuring distance uniformly over the whole network while other metrics on probability distributions fail to do so (e.g total variation, Kullback–Leibler divergence, see [5]). This opens up the potential of mathematical optimisation in the setting of complexity science.

scholarly journals Narratives Transcending Borders: Sabrina Janesch’s "Katzenberge" as a German Response to Polish Migration Literature

2020 ◽  
Vol 47 (2) ◽  
pp. 157-171
Author(s):  
Stephen Naumann
Keyword(s):  
World War Ii ◽  
Forced Migration ◽  
World War ◽  
Polish Spaces ◽  
Migration Literature ◽  
Polish Migration ◽  
Eastern Border ◽  
Border Narratives

The establishment of the Oder-Neisse border between Poland and Germany, as well as the westward shift of Poland’s eastern border resulted in migration for tens of millions in regions that had already been devastated by nearly a decade of forced evacuation, flight, war and genocide. In Poland, postwar authors such as Gdańsk’s own Stefan Chwin and Paweł Huelle have begun to establish a fascinating narrative connecting now-Polish spaces with what are at least in part non-Polish pasts. In Germany, meanwhile, coming to terms with a past that includes the Vertreibung, or forced migration, of millions of Germans during the mid-1940s has been limited at best, in no small part on account of its implication of Germans in the role of victim. In her 2010 debut novel Katzenberge, however, German author Sabrina Janesch employs a Polish migration story to connect with her German readers. Her narrator, like Janesch herself, is a young German who identifies with her Polish grandfather, whose death prompts her to trace the steps of his flight in 1945 from a Galician village to (then) German Silesia. This narrative, I argue, resonates with Janesch’s German audience because the expulsion experience is one with which they can identify. That it centers on Polish migration, however, not only avoids the context of guilt associated with German migration during World War II, but also creates an opportunity to better comprehend their Polish neighbors as well as the geographical spaces that connect them. Instead of allowing border narratives to be limited by the very border they attempt to define, engaging with multiple narratives of a given border provide enhanced meanings in local and national contexts and beyond. 

Sign in / Sign up

Export Citation Format

Share Document