Homeomorphism groups of manifolds and Erdős space.
Homological characterization of boundary set complements
Homotopic homeomorphisms of infinite-dimensional manifolds
Hyperspaces of Finite Sets in Universal Spaces for Absolute Borel Classes
By Fin(X) (resp. ), we denote the hyperspace of all non-empty finite subsets of X (resp. consisting of at most k points) with the Vietoris topology. Let ℓ₂(τ) be the Hilbert space with weight τ and the linear span of the canonical orthonormal basis of ℓ₂(τ). It is shown that if or E is an absorbing set in ℓ₂(τ) for one of the absolute Borel classes and of weight ≤ τ (α > 0) then Fin(E) and each are homeomorphic to E. More generally, if X is a connected E-manifold then Fin(X) is homeomorphic...
Hyperspaces of infinite-dimensional compacta
Hyperspaces of Peano continua are Hubert cubes
Hyperspaces of Peano continua of euclidean spaces
If X is a space then L(X) denotes the subspace of C(X) consisting of all Peano (sub)continua. We prove that for n ≥ 3 the space is homeomorphic to , where B denotes the pseudo-boundary of the Hilbert cube Q.
Indépendance linéaire et classification topologique des espaces normés
Interplay between strongly universal spaces and pairs [Book]
Intersection lattices and topological structures of complements of arrangements in
Les hyperespaces des rétractes absolus et des rétractes absolus de voisinage du plan
Les voisinages ouverts réguliers : critères homotopiques d'existence
L'invariance topologique du type simple d'homotopie
On Cartesian factors and the topological classification of linear metric spaces
On CE-images of the Hubert cube and characterization of Q-manifolds
On closed sets with convex projections in Hilbert space
Let k be a fixed natural number. We show that if C is a closed and nonconvex set in Hilbert space such that the closures of the projections onto all k-hyperplanes (planes with codimension k) are convex and proper, then C must contain a closed copy of Hilbert space. In order to prove this result we introduce for convex closed sets B the set consisting of all points of B that are extremal with respect to projections onto k-hyperplanes. We prove that is precisely the intersection of all k-imitations...
On Countable Dense and Strong Local Homogeneity
We present an example of a connected, Polish, countable dense homogeneous space X that is not strongly locally homogeneous. In fact, a nontrivial homeomorphism of X is the identity on no nonempty open subset of X.
On extension of functors
A. Chigogidze defined for each normal functor on the category Comp an extension which is a normal functor on the category Tych. We consider this extension for any functor on the category Comp and investigate which properties it preserves from the definition of normal functor. We investigate as well some topological properties of such extension.
On infinite-dimensional manifolds
On some applications of infinite-dimensional manifolds to the theory of shape