The Combinatorics of Borel Covers

نویسندگان

  • MARION SCHEEPERS
  • BOAZ TSABAN
چکیده

In this paper we extend previous studies of selection principles for families of open covers of sets of real numbers to also include families of countable Borel covers. The main results of the paper could be summarized as follows: (1) Some of the classes which were different for open covers are equal for Borel covers – Section 1; (2) Some Borel classes coincide with classes that have been studied under a different guise by other authors – Section 4.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Determinacy Approach to Borel Combinatorics

We introduce a new method, involving infinite games and Borel determinacy, which we use to answer several well-known questions in Borel combinatorics.

متن کامل

Hyperfiniteness and Borel Combinatorics

We study the relationship between hyperfiniteness and problems in Borel graph combinatorics by adapting game-theoretic techniques introduced by Marks to the hyperfinite setting. We compute the possible Borel chromatic numbers and edge chromatic numbers of bounded degree acyclic hyperfinite Borel graphs and use this to answer a question of Kechris and Marks about the relationship between Borel c...

متن کامل

Five-value rich lines‎, ‎Borel directions and uniqueness of meromorphic functions

For a meromorphic function $f$ in the complex plane, we shall introduce the definition of five-value rich line of $f$, and study the uniqueness of meromorphic functions of finite order in an angular domain by involving the five-value rich line and Borel directions. Finally, the relationship between a five-value rich line and a Borel direction is discussed, that is, every Borel direction of $f$ ...

متن کامل

Descriptive Graph Combinatorics

In this article we survey the emerging field of descriptive graph combinatorics. This area has developed in the last two decades or so at the interface of descriptive set theory and graph theory, and it has interesting connections with other areas such as ergodic theory and probability theory. Our object of study is the theory of definable graphs, usually Borel or analytic graphs on Polish spac...

متن کامل

Generalizations of Borel-Cantelli Lemma

The Borel-Cantelli Lemma is very important in the probability theory‎. ‎In this paper‎, ‎we first describe the general case of the Borel-Cantelli Lemma‎. ‎The first part of this lemma‎, ‎assuming convergence and the second part includes divergence and independence assumptions‎. ‎In the following‎, ‎we have brought generalizations of the first and second part of this lemma‎. ‎In most generalizat...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008