Characterizing Hilbert space topology in terms of strong negligibility
Characterizing infinite dimensional manifolds topologically
Characterizing metric spaces whose hyperspaces are homeomorphic to ℓ₂
It is shown that the hyperspace (resp. ) of non-empty closed (resp. closed and bounded) subsets of a metric space (X,d) is homeomorphic to ℓ₂ if and only if the completion X̅ of X is connected and locally connected, X is topologically complete and nowhere locally compact, and each subset (resp. each bounded subset) of X is totally bounded.
Classification of function spaces with the pointwise topology determined by a countable dense set
Compact absolute retracts as factors of the Hilbert space
Connecting direct limit topologies with metrics on infinite-dimensional manifolds
Connections on infinite dimensional manifolds with corners
Contractibilité du groupe linéaire des espaces de Hilbert de dimension infinie
Cross-sections of solution funnels in Banach spaces
Densidad de la transversalidad en multijets de variedades con borde anguloso.
Exotic ANR's via null decompositions of Hilbert cube manifolds
Extending Maps in Hilbert Manifolds
Certain results on extending maps taking values in Hilbert manifolds by maps which are close to being embeddings are presented. Sufficient conditions on a map under which it is extendable by an embedding are given. In particular, it is shown that if X is a completely metrizable space of topological weight not greater than α ≥ ℵ₀, A is a closed set in X and f: X → M is a map into a manifold M modelled on a Hilbert space of dimension α such that , then for every open cover of M there is a map g:...
Extension properties of Stone-Čech coronas and proper absolute extensors
We characterize, in terms of X, the extensional dimension of the Stone-Čech corona βX∖X of a locally compact and Lindelöf space X. The non-Lindelöf case is also settled in terms of extending proper maps with values in , where L is a finite complex. Further, for a finite complex L, an uncountable cardinal τ and a -set X in the Tikhonov cube we find a necessary and sufficient condition, in terms of , for X to be in the class AE([L]). We also introduce a concept of a proper absolute extensor and...
-absorbing sequences in hyperspaces of subcontinua
Let denote a true dimension function, i.e., a dimension function such that for all . For a space , we denote the hyperspace consisting of all compact connected, non-empty subsets by . If is a countable infinite product of non-degenerate Peano continua, then the sequence is -absorbing in . As a consequence, there is a homeomorphism such that for all , , where denotes the pseudo boundary of the Hilbert cube . It follows that if is a countable infinite product of non-degenerate...
Fake topological Hilbert spaces and characterizations of dimension in terms of negligibility
Fibering Hilbert cube manifolds over ANRs
Finite-to-one restrictions of continuous functions
Functor of extension in Hilbert cube and Hilbert space
It is shown that if Ω = Q or Ω = ℓ 2, then there exists a functor of extension of maps between Z-sets in Ω to mappings of Ω into itself. This functor transforms homeomorphisms into homeomorphisms, thus giving a functorial setting to a well-known theorem of Anderson [Anderson R.D., On topological infinite deficiency, Michigan Math. J., 1967, 14, 365–383]. It also preserves convergence of sequences of mappings, both pointwise and uniform on compact sets, and supremum distances as well as uniform continuity,...
Geometrical and topological properties of bumps and starlike bodies in Banach spaces.
Hilbert cube modulo an arc