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L J -spaces

Yin-Zhu Gao (2007)

Czechoslovak Mathematical Journal

In this paper L J -spaces are introduced and studied. They are a common generalization of Lindelöf spaces and J -spaces researched by E. Michael. A space X is called an L J -space if, whenever { A , B } is a closed cover of X with A B compact, then A or B is Lindelöf. Semi-strong L J -spaces and strong L J -spaces are also defined and investigated. It is demonstrated that the three spaces are different and have interesting properties and behaviors.

La genèse du théorème de recouvrement de Borel

Bernard Maurey, Jean-Pierre Tacchi (2005)

Revue d'histoire des mathématiques

Nous nous proposons de rendre à Émile Borel le mérite d’avoir considéré le premier un recouvrement d’un segment de droite par une suite infinie d’intervalles et prouvé que l’on peut en extraire un sous-recouvrement fini. L’appellation de théorème de Heine-Borel souvent donnée à ce résultat, en référence à un article de Heine de 1872, conduit à sous-estimer les différences avec le théorème sur la continuité uniforme (dont une première version peut être attribuée à Dirichlet, en 1854) ; cette dénomination...

Locally constant functions

Joan Hart, Kenneth Kunen (1996)

Fundamenta Mathematicae

Let X be a compact Hausdorff space and M a metric space. E 0 ( X , M ) is the set of f ∈ C(X,M) such that there is a dense set of points x ∈ X with f constant on some neighborhood of x. We describe some general classes of X for which E 0 ( X , M ) is all of C(X,M). These include βℕ, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. In the case where M is a Banach space, we discuss the properties of E 0 ( X , M ) as a normed linear space. We also build three first countable Eberlein...

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