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Displaying 21 – 36 of 36

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.

Normality and Martin's axiom

K. Alster, T. Przymusiński (1976)

Fundamenta Mathematicae

Normality and paracompactness in subsets of product spaces

Teodor Przymusiński (1976)

Fundamenta Mathematicae

Normality and paracompactness of Pixley-Roy hyperspaces

Teodor Przymusiński (1981)

Fundamenta Mathematicae

Note on a result of E.P. Lane

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

Portugaliae mathematica

Note on category in Cartesian products of metrizable spaces

Roman Pol (1979)

Fundamenta Mathematicae

Note on decompositions of metrizable spaces I

Roman Pol (1977)

Fundamenta Mathematicae

Note on decompositions of metrizable spaces II

Roman Pol (1978)

Fundamenta Mathematicae

Note on extremal points

Downing, J.R., White, A.G. (1974)

Portugaliae mathematica

Note on limits of simply continuous and cliquish functions.

Ewert, Janina (1994)

International Journal of Mathematics and Mathematical Sciences

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 $c f p$ -covers

Shou Lin, Peng Fei Yan (2003)

Commentationes Mathematicae Universitatis Carolinae

The main purpose of this paper is to establish general conditions under which $T_{2}$ -spaces are compact-covering images of metric spaces by using the concept of $c f p$ -covers. We generalize a series of results on compact-covering open images and sequence-covering quotient images of metric spaces, and correct some mapping characterizations of $g$ -metrizable spaces by compact-covering $σ$ -maps and $m s s c$ -maps.

Displaying 21 – 36 of 36

Normal Vietoris implies compactness: a short proof

Normality and Martin's axiom

Normality and paracompactness in subsets of product spaces

Normality and paracompactness of Pixley-Roy hyperspaces

Note on a result of E.P. Lane

Note on category in Cartesian products of metrizable spaces

Note on decompositions of metrizable spaces I

Note on decompositions of metrizable spaces II

Note on extremal points

Note on limits of simply continuous and cliquish functions.

Note on metrization of quasi-uniform spaces

Note on quasi-uniform spaces and representable spaces

Notes on $c f p$ -covers

Notes on Fréchet spaces.

Notes on the topologies and uniformities of hyperspaces

Numerical invariants of 0-dimensional spaces and their Cartesian multiplication.

Currently displaying 21 – 36 of 36