Retracts and homotopies for multi-maps
Retracts of Tychonoff and normal spaces.
Selections and near-selections in metric linear spaces without local convexity
We characterize the AR property in convex subsets of metric linear spaces in terms of certain near-selections.
Several characterizations of SSDR-maps
Shape morphisms and spaces of approximative maps
Shapes of finite-dimensional compacta
Size levels for arcs
We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.
Solution du problème de point fixe de Schauder
We give an affirmative answer to Schauder's fixed point question.
Solution d'un probleme de Fadell sur les fibres
Let E be the total space of a Hurewicz fiber space whose base and all fibers are ANRs. We prove that if E is metrisable, then it is also an ANR.
Some extension and classification theorems for maps of movable spaces
Some theorems about the embeddability of ANR-sets into decomposition spaces of
Some theorems and examples on local equiconnectedness and its specializations
Spaces of ANR's
Spaces of ANR's. II
Spaces of measurable functions
For a metrizable space X and a finite measure space (Ω, , µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of -measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point.
Sur la somme et le produit combinatoire des rétractes absolus
Sur le prolongement des fonctions continues dans les complexes simpliciaux infinis
Sur les rétractes absolus Pn -valués de dimension finie
We prove that a k-dimensional hereditarily indecomposable metrisable continuum is not a -valued absolute retract. We deduce from this that none of the classical characterizations of ANR (metric) extends to the class of stratifiable spaces.
Symmetrie Products of ANR's.
The ANR-property of hyperspaces with the Attouch-Wets topology
We characterize metric spaces whose hyperspaces of non-empty closed, bounded, compact or finite subsets, endowed with the Attouch-Wets topology, are absolute (neighborhood) retracts.