The combinatorics of Borel covers

By Marion Scheepers, Boaz Tsaban. 2002

94 citations recorded by the source corpus.

Abstract 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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3ea7f6d169cad3e707be2b3f9dee96c803e80320

How researchers see this paper

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In Computational Theory and Mathematics

1. Boaz Tsaban
2. Tomek Bartoszynski
3. Franklin D. Tall
4. Marion Scheepers
5. L. Kočinac

In Geometry and Topology

1. Boaz Tsaban
2. Tomek Bartoszynski
3. Franklin D. Tall
4. Marion Scheepers
5. L. Kočinac
6. Giuseppe Di Maio
7. Lubomyr Zdomsky

In Mathematical Physics

1. Boaz Tsaban
2. Tomek Bartoszynski
3. Marion Scheepers
4. Franklin D. Tall
5. L. Kočinac
6. Giuseppe Di Maio

Citations in the corpus

• Selected results on selection principles (2012, unknown): “Selection Property Game Partition relation Source 1 S1(O,O) G1(O,O) Ω → (Λ) 2 m [58], [69] 2 S1(Ω,Ω) G1(Ω,Ω) Ω → (Ω) n m [70], [69] 3 S1(B,B) G1(B,B) BΩ → (B) 2 m [75] 4 S1(K,K) ? K → (K) 2 2 [20] 5 S1(Ω,Γ) G1(Ω,Γ) Ω → (Γ) 2 m [30], [69] 6 S1(K,Γ) G1(K,Γ) K → (Γ) n m [20], [17] 7 S1(K,Γk) G1(K,Γk) K”
• Lindelöf indestructibility, topological games and selection principles (2009, background): “Some properties of this class of Hurewicz spaces can be found in [44], such as that such subsets of the real line are zero-dimensional and that Sierpiński sets are strongly Hurewicz.”
• Selection principles and the Minimal Tower problem (2001, methodology): “Following [7] and [13], we consider the following types of covers: O (respectively, B): The collection of countable open (respectively, Borel) covers of X .”
• Selection principles and covering properties in Topology (2003, unknown): “nonR(Property) Property Source p S1(ΩX ,ΓX) [30] Sfin(ΩX ,TX) [89] max{s, b} S1(TX ,ΓX) [77] r Ufin(ΓX ,TX) [89] split(ΛX ,ΛX) [43] u split(ΩX ,ΩX) [43] add(M) S1(ΩX ,O X ) [54] cov(M) S1(OX ,OX) [29] S1(ΩX ,ΩX) [43] b Sfin(ΩX ,O X ) [42] S1(ΓX ,ΓX) [43] d Sfin(OX ,OX) [42] Sfin(ΩX ,ΩX) [43] Sfin(ΩX”
• Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures (2002, background): “We describe two nontrivial examples which are in particular counter-examples to conjectures of Menger and Hurewicz.”