Hyperspaces of CW-complexes
It is shown that the hyperspace of a connected CW-complex is an absolute retract for stratifiable spaces, where the hyperspace is the space of non-empty compact (connected) sets with the Vietoris topology.
Inaccessibility, essential maps, and shape theory
Injectivity of polyhedra
Intersections of ANR's
Inverse Sequences and Absolute Co-Extensors
Suppose that K is a CW-complex, X is an inverse sequence of stratifiable spaces, and X = limX. Using the concept of semi-sequence, we provide a necessary and sufficient condition for X to be an absolute co-extensor for K in terms of the inverse sequence X and without recourse to any specific properties of its limit. To say that X is an absolute co-extensor for K is the same as saying that K is an absolute extensor for X, i.e., that each map f:A → K from a closed subset A of X extends to a map F:X...
Investigating the ANR-property of metric spaces
La théorie des points fixes des applications à itérée condensante
La théorie des rétracts approximatifs et le théorème des points fixes de Lefschetz [Book]
Le théorème de Lefschetz pour les ANR approximatifs
Les voisinages ouverts réguliers : critères homotopiques d'existence
Limiting subcontinua and Whitney maps of tree-like continua
Local cohomological properties of homogeneous ANR compacta
In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR continuum and x ∈ X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of Ū and bd U are similar to the properties of the closed ball ⁿ ⊂ ℝⁿ and its boundary . We also prove that a metric ANR compactum X of dimension n is dimensionally full-valued if and only if the group Hₙ(X,X∖x;ℤ) is not trivial for some x ∈ X. This implies that...
Locally admissible multi-valued maps
In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.
Locally compact spaces C-tame at infinity.
Locally Compact Spaces ℓ-Tame At Infinity
Locally equiconnected spaces and absolute neighborhood retracts
Locally well-behaved paracompacta in shape theory
Locallyn-Connected Compacta and UV n -Maps
We provide a machinery for transferring some properties of metrizable ANR-spaces to metrizable LCn-spaces. As a result, we show that for completely metrizable spaces the properties ALCn, LCn and WLCn coincide to each other. We also provide the following spectral characterizations of ALCn and celllike compacta: A compactum X is ALCn if and only if X is the limit space of a σ-complete inverse system S = {Xα , pβ α , α < β < τ} consisting of compact metrizable LCn-spaces Xα such that all bonding...
ℓp-Movable At Infinity Spaces, Compact And Divisors And Property UVWn
Mapping approximate inverse systems of compacta