6 research outputs found
Functor of continuation in Hilbert cube and Hilbert space
A -set in a metric space is a closed subset of such that each
map of the Hilbert cube into can uniformly be approximated by maps of
into . The aim of the paper is to show that there exists a
functor of extension of maps between -sets of [or ] to maps acting
on the whole space [resp. ]. Special properties of the functor are
proved.Comment: 9 page
Normal systems over ANR's, rigid embeddings and nonseparable absorbing sets
Most of results of Bestvina and Mogilski [\textit{Characterizing certain
incomplete infinite-dimensional absolute retracts}, Michigan Math. J.
\textbf{33} (1986), 291--313] on strong -sets in ANR's and absorbing sets is
generalized to nonseparable case. It is shown that if an ANR is locally
homotopy dense embeddable in infinite-dimensional Hilbert manifolds and (where `' is the topological weight) for each open nonempty subset
of ,then itself is homotopy dense embeddable in a Hilbert manifold. It
is also demonstrated that whenever is an AR, its weak product is
homeomorphic to a pre-Hilbert space with . An intrinsic
characterization of manifolds modelled on such pre-Hilbert spaces is given.Comment: 26 page