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Quasi-equivalence of compacta and spaces of components.

José M. Rodríguez Sanjurjo (1980)

Collectanea Mathematica

Let X, Y be two compacta with Sh(X) = Sh (Y). Then, the spaces of components of X, Y are homeomorphic. This does not happen, in general, when X, Y are quasi-equivalent. In this paper we give a sufficient condition for the existence of a homeomorphism between the spaces of components of two quasi-equivalent compacta X, Y which maps each component in a quasi-equivalent component.

Quasi-metrization and completion for Pervin's quasi-uniformity.

V. Gregori, J. Ferrer (1982)

Stochastica

R. Stoltenberg characterized in [2] those quasi-uniformities which are quasi-pseudometrizable, as well as those quasi-metric spaces which have a quasi-metric completion. In this paper we follow Stoltenberg's work by giving characterizations for quasi-metrizability and quasi-metric completion for a particular type of quasi-uniform spaces, the Pervin's quasi-uniform space.

Quasi-uniform Space

Roland Coghetto (2016)

Formalized Mathematics

In this article, using mostly Pervin [9], Kunzi [6], [8], [7], Williams [11] and Bourbaki [3] works, we formalize in Mizar [2] the notions of quasiuniform space, semi-uniform space and locally uniform space. We define the topology induced by a quasi-uniform space. Finally we formalize from the sets of the form ((X Ω) × X) ∪ (X × Ω), the Csaszar-Pervin quasi-uniform space induced by a topological space.

Quelques propriétés des espaces α -favorables et applications aux convexes compacts

Gabriel Debs (1980)

Annales de l'institut Fourier

Soit X un espace topologique régulier et fortement α -favorable : si X est image continue d’un espace métrisable séparable alors X est lusinien; ceci répond à une question de R. Haydon. Si X est seulement de Lindelöf et à diagonale G δ alors l’espace mesurable ( X , B a ( X ) ) ) est standard; on en déduit que si l’ensemble des points extrêmaux d’un convexe compact K est de Lindelöf et à diagonale G δ , alors K est métrisable.

Questions

Alexey Ostrovsky (2005)

Acta Universitatis Carolinae. Mathematica et Physica

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