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Displaying 181 – 200 of 418

Normal Vietoris implies compactness: a short proof

G. Di Maio, E. Meccariello, Somashekhar Naimpally (2004)

Czechoslovak Mathematical Journal

One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.

Note on a result of E.P. Lane

Fletcher, P., Lindgren, W.F. (1976)

Portugaliae mathematica

Note on metrization of quasi-uniform spaces

P. Fletcher (1971)

Colloquium Mathematicae

Note on quasi-uniform spaces and representable spaces

P. Fletcher (1971)

Colloquium Mathematicae

Notes on the topologies and uniformities of hyperspaces

Giuliano Artico, Roberto Moresco (1980)

Rendiconti del Seminario Matematico della Università di Padova

On a certain class of $Λ$ -structures. I

Stanislav Tomášek (1970)

Czechoslovak Mathematical Journal

On a certain class of $Λ$ -structures. II

Stanislav Tomášek (1970)

Czechoslovak Mathematical Journal

On a Class of Darboux Functions from a Topological Space to a Uniform Space

Beloslav Riečan (1971)

Matematický časopis

On a class of real normed lattices

C. Alegre, Jesús Ferrer, Valentín Gregori (1998)

Czechoslovak Mathematical Journal

We say that a real normed lattice is quasi-Baire if the intersection of each sequence of monotonic open dense sets is dense. An example of a Baire-convex space, due to M. Valdivia, which is not quasi-Baire is given. We obtain that $E$ is a quasi-Baire space iff $(E, T (𝒰), T (𝒰^{- 1}))$ , is a pairwise Baire bitopological space, where $𝒰$ , is a quasi-uniformity that determines, in $L$ . Nachbin’s sense, the topological ordered space $E$ .