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Quasi-orbit spaces associated to T₀-spaces

C. Bonatti, H. Hattab, E. Salhi (2011)

Fundamenta Mathematicae

Let G ⊂ Homeo(E) be a group of homeomorphisms of a topological space E. The class of an orbit O of G is the union of all orbits having the same closure as O. Let E/G̃ be the space of classes of orbits, called the quasi-orbit space. We show that every second countable T₀-space Y is a quasi-orbit space E/G̃, where E is a second countable metric space. The regular part X₀ of a T₀-space X is the union of open subsets homeomorphic to ℝ or to 𝕊¹. We give a characterization of the spaces X with finite...

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.

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