The functor of weakly additive functionals of finite degree.
The hyperspace of finite subsets of a stratifiable space
It is shown that the hyperspace of non-empty finite subsets of a space X is an ANR (an AR) for stratifiable spaces if and only if X is a 2-hyper-locally-connected (and connected) stratifiable space.
The hyperspace of lower semicontinuity and the first power of a topological space
The LCC-topology on the space of continuous functions
The lifting property for classes of mappings.
The nonexistence of expansive homeomorphisms of chainable 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 . In this paper, we prove that if a homeomorphism f:X → X of a continuum X can be lifted to an onto map h:P → P of the pseudo-arc P, then f is not expansive. As a corollary, we prove that there are no expansive homeomorphisms on chainable continua. This is an affirmative answer to one of Williams’ conjectures.
The openness of induced maps on hyperspaces
The operation of infimal convolution [Book]
The set functions 𝓣 and 𝒦 and irreducible continua
We study the set functions 𝓣 and 𝒦 on irreducible continua. We present several properties of these functions when defined on irreducible continua. In particular, we characterize the class of irreducible continua for which these functions are continuous. We also characterize the class of 𝒦-symmetric irreducible continua.
The space of ANR’s in
The hyperspaces and in consisting respectively of all compact absolute neighborhood retracts and all compact absolute retracts are studied. It is shown that both have the Borel type of absolute -spaces and that, indeed, they are not -spaces. The main result is that is an absorber for the class of all absolute -spaces and is therefore homeomorphic to the standard model space of this class.
The Spaces of Closed Convex Sets in Euclidean Spaces with the Fell Topology
Let be the space of all non-empty closed convex sets in Euclidean space ℝ ⁿ endowed with the Fell topology. We prove that for every n > 1 whereas .
The structure of atoms (hereditarily indecomposable continua)
Let X be an atom (= hereditarily indecomposable continuum). Define a metric ϱ on X by letting where is the (unique) minimal subcontinuum of X which contains x and y and W is a Whitney map on the set of subcontinua of X with W(X) = 1. We prove that ϱ is an ultrametric and the topology of (X,ϱ) is stronger than the original topology of X. The ϱ-closed balls C(x,r) = y ∈ X:ϱ ( x,y) ≤ r coincide with the subcontinua of X. (C(x,r) is the unique subcontinuum of X which contains x and has Whitney value...
Three variants of a Kuratowski's theorem
Topological properties of a new graph topology.
Topologie su spazi di funzioni derivanti da topologie su iperspazi
Topologie sur l'ensemble des compacts non vides d'un espace topologique séparé. Exemple de complémentaire analytique non analytique dans un espace polonais
Topologizing the hypersets.
Typical sets and typical continuous functions
Ultraparacompactness in certain Pixley-Roy hyperspaces
Uniformities, Hyperspaces, and Normality.