Displaying similar documents to “Selections and approaching points in products”

Composition of axial functions of products of finite sets

Krzysztof Płotka (2007)

Colloquium Mathematicae

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We show that every function f: A × B → A × B, where |A| ≤ 3 and |B| < ω, can be represented as a composition f₁ ∘ f₂ ∘ f₃ ∘ f₄ of four axial functions, where f₁ is a vertical function. We also prove that for every finite set A of cardinality at least 3, there exist a finite set B and a function f: A × B → A × B such that f ≠ f₁ ∘ f₂ ∘ f₃ ∘ f₄ for any axial functions f₁, f₂, f₃, f₄, whenever f₁ is a horizontal function.

The crossing numbers of certain Cartesian products

Marián Klešč (1995)

Discussiones Mathematicae Graph Theory

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In this article we determine the crossing numbers of the Cartesian products of given three graphs on five vertices with paths.

The fixed point property for some cartesian products

Roman Mańka (2001)

Fundamenta Mathematicae

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It is proved that the cylinder X × I over a planar λ-dendroid X has the fixed point property. This is a partial solution of two problems posed by R. H. Bing (cf. [1], Questions 9 and 10).