Displaying similar documents to “On strongly sum-free subsets of abelian groups”

Linear extensions of relations between vector spaces

Árpád Száz (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let X and Y be vector spaces over the same field K . Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation F of X into Y is called linear if λ F ( x ) ⊂ F ( λ x ) and F ( x ) + F ( y ) ⊂ F ( x + y ) for all λ ∈ K ∖ { 0 } and x , y ∈ X . After improving and supplementing some former results on linear relations, we show that a relation Φ of a linearly independent subset E of X into Y can be extended to a linear relation F of X into Y if and only if there exists a linear subspace Z of Y such that Φ ( e ) ∈ Y | Z for all e ∈ E . Moreover, if...

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.

G δ -modification of compacta and cardinal invariants

Aleksander V. Arhangel'skii (2006)

Commentationes Mathematicae Universitatis Carolinae

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Given a space X , its G δ -subsets form a basis of a new space X ω , called the G δ -modification of X . We study how the assumption that the G δ -modification X ω is homogeneous influences properties of X . If X is first countable, then X ω is discrete and, hence, homogeneous. Thus, X ω is much more often homogeneous than X itself. We prove that if X is a compact Hausdorff space of countable tightness such that the G δ -modification of X is homogeneous, then the weight w ( X ) of X does not exceed 2 ω (Theorem 1)....

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...