Universally Kuratowski–Ulam spaces and open-open games

Journal Title: Annales Mathematicae Silesianae - Year 2015, Vol 29, Issue

Abstract

We examine the class of spaces in which the second player has a winning strategy in the open-open game. We show that this spaces are not universally Kuratowski–Ulam. We also show that the games $G$ and $G_7$ introduced by P. Daniels, K. Kunen, H. Zhou [Fund. Math. 145 (1994), no. 3, 205–220] are not equivalent.

Authors and Affiliations

Piotr Kalemba, Andrzej Kucharski

Keywords

Related Articles

Solutions and stability of generalized Kannappan’s and Van Vleck’s functional equations

We study the solutions of the integral Kannappan’s and Van Vleck’s functional equations $$∫_{S}f(xyt)dμ(t) +∫_{S}f(xσ(y)t)dμ(t) = 2f(x)f(y), x,y∈S;$$ $$∫_{S}f(xσ(y)t)dμ(t)−∫_{S}f(xyt)dμ(t) = 2f(x)f(y), x,y∈S,$$ where $...

On the general and measurable solutions of some functional equations

The general solutions of two functional equations, without imposing any regularity condition on any of the functions appearing, have been obtained. From these general solutions, the Lebesgue measurable solutions have bee...

Mathematical challenges in the theory of chemotaxis

We consider the simplest parabolic-elliptic model of chemotaxisin the whole space and in several space dimensions. Criteria either for theexistence of radial global-in-time solutions or their blowup in terms of suitable...

A simple proof of the Polar Decomposition Theorem

In this expository paper, we present a new and easier proof of the Polar Decomposition Theorem. Unlike in classical proofs, we do not use the square root of a positive matrix. The presented proof is accessible to a broad...

An application of the theory of scale of Banach spaces

The abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the s...

Download PDF file
  • EP ID EP230405
  • DOI 10.1515/amsil-2015-0007
  • Views 170
  • Downloads 0

How To Cite

Piotr Kalemba, Andrzej Kucharski (2015). Universally Kuratowski–Ulam spaces and open-open games. Annales Mathematicae Silesianae, 29(), 85-92. https://europub.co.uk./articles/-A-230405