Displaying similar documents to “Application of covering sets”

A topological version of Bertini's theorem

Artur Piękosz (1995)

Annales Polonici Mathematici

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We give a topological version of a Bertini type theorem due to Abhyankar. A new definition of a branched covering is given. If the restriction π V : V → Y of the natural projection π: Y × Z → Y to a closed set V ⊂ Y × Z is a branched covering then, under certain assumptions, we can obtain generators of the fundamental group π₁((Y×Z).

On D-dimension of metrizable spaces

Wojciech Olszewski (1991)

Fundamenta Mathematicae

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For every cardinal τ and every ordinal α, we construct a metrizable space M α ( τ ) and a strongly countable-dimensional compact space Z α ( τ ) of weight τ such that D ( M α ( τ ) ) ≤ α , D ( Z α ( τ ) ) ≤ α and each metrizable space X of weight τ such that D(X) ≤ α is homeomorphic to a subspace of M α ( τ ) and to a subspace of Z α + 1 ( τ ) .

Uniformly completely Ramsey sets

Udayan Darji (1993)

Colloquium Mathematicae

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Galvin and Prikry defined completely Ramsey sets and showed that the class of completely Ramsey sets forms a σ-algebra containing open sets. However, they used two definitions of completely Ramsey. We show that they are not equivalent as they remarked. One of these definitions is a more uniform property than the other. We call it the uniformly completely Ramsey property. We show that some of the results of Ellentuck, Silver, Brown and Aniszczyk concerning completely Ramsey sets also...