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 Dominique Lecomte Mathematics , 2007, Abstract: We give, for some Borel sets of a product of two Polish spaces, including the Borel sets with countable sections, a Hurewicz-like characterization of those which cannot become a transfinite difference of open sets by changing the two Polish topologies.
 Mathematics , 2002, Abstract: We prove a new selection theorem for multivalued mappings of C-space. Using this theorem we prove extension dimensional version of Hurewicz theorem for a closed mapping $f\colon X\to Y$ of $k$-space $X$ onto paracompact $C$-space $Y$: if for finite $CW$-complex $M$ we have $\ed Y\le [M]$ and for every point $y\in Y$ and every compactum $Z$ with $\ed Z\le [M]$ we have $\ed(f^{-1}(y)\times Z)\le [L]$ for some $CW$-complex $L$, then $\ed X\le [L]$.
 Liljana Babinkostova Mathematics , 2007, Abstract: We characterize the Hurewicz covering property in metrizable spaces in terms of properties of the metrics of the space. Then we show that a weak version of selective screenability, when combined with the Hurewicz property, implies selective screenability.
 Constantin Felicia Annals of the University of Oradea : Economic Science , 2010, Abstract: La dynamique de la société actuelle privilégie la libre circulation des personnes et de l'information. L'Europe, sans les frontières physiques qui séparaient autrefois les peuples, fournit le sentiment naturel d'un espace global, aujourd'hui violemment frappé par la crise économique. Dans le contexte des réductions des budgets, les entreprises doivent se redresser par l'implémentation de stratégies compétitives. Le modèle de la roue compétitive de Marc Ingham permet d'envisager les ressources humaines et leurs compétences linguistiques comme une valeur ajoutée, facteur stratégique révélateur de différences. La formation langagière étant cependant dispendieuse, nous suggérons une solution équilibrée et économique: la formation aux compétences partielles en langues étrangères par l'intercompréhension linguistique.
 Sylvain Palfroy Criminocorpus, Revue Hypermédia , 2007, DOI: 10.4000/criminocorpus.244 Abstract: Le premier plan de The Lodger, - film considéré par Hitchcock comme son véritable premier film (chronologiquement son 3e), le premier Hitchcock picture comme il le dit à Fran ois Truffaut - montre en gros plan le visage d’une femme hurlant. Ce plan condense en lui une grande partie des éléments qui vont constituer la matière de l’ uvre : la femme, le sexe, le meurtre. Ce qui retient l’attention dans ce plan au-delà du cri - qui renvoie comme bien des cris cadrés par le cinéaste au célèbr...
 Revista Colombiana de Matemáticas , 2005, Abstract: this paper we provides an alternative proof of hurewicz theorem when the topological space x is a cw-complex. indeed, we show that if x0 c x1 c ... xn-1 c xn = x is the cw decomposition of x, then the hurewicz homomorphism ∏n+1 (xn+1,xn) → hn+1 (xn+1,xn) is an isomorphism, and together with a result from homological algebra we prove that if x is (n-1)-connected, the hurewicz homomorphism ∏n (x) → hn (x) is an isomorphism.
 Revista Colombiana de Matemáticas , 2005, Abstract: This paper we provides an alternative proof of Hurewicz theorem when the topological space X is a CW-complex. Indeed, we show that if X0 C X1 C ... Xn-1 C Xn = X is the CW decomposition of X, then the Hurewicz homomorphism ∏n+1 (Xn+1,Xn) → Hn+1 (Xn+1,Xn) is an isomorphism, and together with a result from Homological Algebra we prove that if X is (n-1)-connected, the Hurewicz homomorphism ∏n (X) → Hn (X) is an isomorphism. En este artículo damos una demostración alternativa de el teorema de Hurewicz cuando el espacio topológico X es CW-complejo. En realidad probamos que si X0 C X1 C ... Xn-1 C Xn = X es una descomposición CW de X, el homomorfismo de Hurewicz ∏n+1 (Xn+1,Xn) → Hn+1 (Xn+1,Xn) es un isomorfismo y usando un resultado de álgebra Homológica demostramos que si X es conexo, el homomorfismo de Hurewicz ∏n (X) → Hn (X) es un isomorfismo.
 Boaz Tsaban Mathematics , 2001, Abstract: In classical works, Hurewicz and Menger introduced two diagonalization properties for sequences of open covers. Hurewicz found a combinatorial characterization of these notions in terms of continuous images. Recently, Scheepers has shown that these notions are particular cases in a large family of diagonalization schemas. One of the members of this family is weaker than the Hurewicz property and stronger than the Menger property, and it was left open whether it can be characterized combinatorially in terms of continuous images. We give a positive answer. This paper can serve as an exposition of this fascinating subject.
 Mathematics , 2015, Abstract: By classical results of Hurewicz, Kechris and Saint-Raymond, an analytic subset of a Polish space $X$ is covered by a $K_\sigma$ subset of $X$ if and only if it does not contain a closed-in-$X$ subset homeomorphic to the Baire space ${}^\omega \omega$. We consider the analogous statement (which we call Hurewicz dichotomy) for $\Sigma^1_1$ subsets of the generalized Baire space ${}^\kappa \kappa$ for a given uncountable cardinal $\kappa$ with $\kappa=\kappa^{<\kappa}$, and show how to force it to be true in a cardinal and cofinality preserving extension of the ground model. Moreover, we show that if the Generalized Continuum Hypothesis (GCH) holds, then there is a cardinal preserving class-forcing extension in which the Hurewicz dichotomy for $\Sigma^1_1$ subsets of ${}^\kappa \kappa$ holds at all uncountable regular cardinals $\kappa$, while strongly unfoldable and supercompact cardinals are preserved. On the other hand, in the constructible universe L the dichotomy for $\Sigma^1_1$ sets fails at all uncountable regular cardinals, and the same happens in any generic extension obtained by adding a Cohen real to a model of GCH. We also discuss connections with some regularity properties, like the $\kappa$-perfect set property, the $\kappa$-Miller measurability, and the $\kappa$-Sacks measurability.
 Mathematics , 2005, DOI: 10.4171/JEMS/132 Abstract: Menger's basis property is a generalization of $\sigma$-compactness and admits an elegant combinatorial interpretation. We introduce a general combinatorial method to construct non $\sigma$-compact sets of reals with Menger's property. Special instances of these constructions give known counterexamples to conjectures of Menger and Hurewicz. We obtain the first explicit solution to the Hurewicz 1927 problem, that was previously solved by Chaber and Pol on a dichotomic basis. The constructed sets generate nontrivial subfields of the real line with strong combinatorial properties, and most of our results can be stated in a Ramsey-theoretic manner. Since we believe that this paper is of interest to a diverse mathematical audience, we have made a special effort to make it self-contained and accessible.
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