Displaying similar documents to “A canonical Ramsey-type theorem for finite subsets of ℕ ”

Combinatorics and quantifiers

Jaroslav Nešetřil (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let I m be the set of subsets of I of cardinality m . Let f be a coloring of I m and g a coloring of I m . We write f → g if every f -homogeneous H ⊆ I is also g -homogeneous. The least m such that f → g for some f : I m → k is called the of g and denoted by w k ( g ) . In the first part of the paper we prove the existence of colorings with high k -width. In particular, we show that for each k > 0 and m > 0 there is a coloring g with w k ( g ) = m . In the second part of the paper we give applications of wide colorings in the theory of generalized...

A β -normal Tychonoff space which is not normal

Eva Murtinová (2002)

Commentationes Mathematicae Universitatis Carolinae

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α -normality and β -normality are properties generalizing normality of topological spaces. They consist in separating dense subsets of closed disjoint sets. We construct an example of a Tychonoff β -normal non-normal space and an example of a Hausdorff α -normal non-regular space.

On α -normal and β -normal spaces

Aleksander V. Arhangel'skii, Lewis D. Ludwig (2001)

Commentationes Mathematicae Universitatis Carolinae

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We define two natural normality type properties, α -normality and β -normality, and compare these notions to normality. A natural weakening of Jones Lemma immediately leads to generalizations of some important results on normal spaces. We observe that every β -normal, pseudocompact space is countably compact, and show that if X is a dense subspace of a product of metrizable spaces, then X is normal if and only if X is β -normal. All hereditarily separable spaces are α -normal. A space is...