Non-unique fixed points in L-spaces.
Normal Vietoris implies compactness: a short proof
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 hereditary countable paracompactness of Pixley-Roy hyperspaces
Normality and paracompactness of Pixley-Roy hyperspaces
Note on the Wijsman hyperspaces of completely metrizable spaces
We consider the hyperspace of nonempty closed subsets of completely metrizable space endowed with the Wijsman topologies . If is separable and , are two metrics generating the topology of , every countable set closed in has isolated points in . For , this implies a theorem of Costantini on topological completeness of . We show that for nonseparable the hyperspace may contain a closed copy of the rationals. This answers a question of Zsilinszky.
Note sur topologie exponentielle
Notes on the topologies and uniformities of hyperspaces
On a compactification of the homeomorphism group of the pseudo-arc
A continuum means a compact connected metric space. For a continuum X, H(X) denotes the space of all homeomorphisms of X with the compact-open topology. It is well known that H(X) is a completely metrizable, separable topological group. J. Kennedy [8] considered a compactification of H(X) and studied its properties when X has various types of homogeneity. In this paper we are concerned with the compactification of the homeomorphism group of the pseudo-arc P, which is obtained by the method of...
On a metrization of the hyperspace of a metric space
On admissible Whitney maps
On approximation of multifunctions with respect to the Vietoris topology
On connectivity properties of bitopological hyperspaces
On connectivity properties of hyperspaces of spaces
On ℳ-contractibility
On convex metric spaces V
On generalized whitney mappings
On Hausdorff intrinsic metric.
On hit-and-miss hyperspace topologies
The Vietoris topology and Fell topologies on the closed subsets of a Hausdorff uniform space are prototypes for hit-and-miss hyperspace topologies, having as a subbase all closed sets that hit a variable open set, plus all closed sets that miss (= fail to intersect) a variable closed set belonging to a prescribed family of closed sets. In the case of the Fell topology, where consists of the compact sets, a closed set misses a member of if and only if is far from in a uniform sense....
On indecomposability and composants of chaotic continua
A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x,y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that . A homeomorphism f: X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ ℤ such that . Clearly, every expansive homeomorphism is continuum-wise expansive, but the converse assertion is not true. In [6], we defined the notion of chaotic continua of homeomorphisms...
On local 1-connectedness of Whitney continua