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More results in polychromatic Ramsey theory

100%

Abraham U., Cummings J.

Open Mathematics

2012

tom 10

nr 3

1004-1016

We study polychromatic Ramsey theory with a focus on colourings of [ω 2]2. We show that in the absence of GCH there is a wide range of possibilities. In particular each of the following is consistent relative to the consistency of ZFC: (1) 2ω = ω 2 and $\omega _2 \to ^{poly} (\alpha )_{\aleph _0 - bdd}^2 $ for every α <ω 2; (2) 2ω = ω 2 and $\omega _2 \nrightarrow ^{poly} (\omega _1 )_{2 - bdd}^2 $ .

On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces

100%

Önal S., Vural Ç.

Open Mathematics

2013

tom 11

nr 9

1635-1642

We introduce the concept of a family of sets generating another family. Then we prove that if X is a topological space and X has W = {W(x): x ∈ X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of ω-rank, then X is metaLindelöf as well as a countable product of them. We also prove that if W satisfies ω-rank (F) and, for every x ∈ X, W(x) is of the form W 0(x) ∪ W 1(x), where W 0(x) is Noetherian and W 1(x) consists of neighbourhoods of x, then X is metacompact.

Ograniczanie wyników

2 Open Mathematics

1 Abraham U.

1 Cummings J.

1 Vural Ç.

1 Önal S.

1 2013

1 2012

Wyniki wyszukiwania

More results in polychromatic Ramsey theory

On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces