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Recouvrements, derivation des mesures et dimensions.

Patrice Assouad, Thierry Quentin de Gromard (2006)

Revista Matemática Iberoamericana

Let X be a set with a symmetric kernel d (not necessarily a distance). The space (X,d) is said to have the weak (resp. strong) covering property of degree ≤ m [briefly prf(m) (resp. prF(m))], if, for each family B of closed balls of (X,d) with radii in a decreasing sequence (resp. with bounded radii), there is a subfamily, covering the center of each element of B, and of order ≤ m (resp. splitting into m disjoint families). Since Besicovitch, covering properties are known to be the main tool for...

Rectangular covers of products missing diagonals

Yukinobu Yajima (1994)

Commentationes Mathematicae Universitatis Carolinae

We give a characterization of a paracompact Σ -space to have a G δ -diagonal in terms of three rectangular covers of X 2 Δ . Moreover, we show that a local property and a global property of a space X are given by the orthocompactness of ( X × β X ) Δ .

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