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A Polish AR-Space with no Nontrivial Isotopy

100%

Dobrowolski T.

nr 1

67-74

The Polish space Y constructed in [vM1] admits no nontrivial isotopy. Yet, there exists a Polish group that acts transitively on Y.

Failure of the Factor Theorem for Borel pre-Hilbert spaces

63%

Dobrowolski T. , Marciszewski W.

tom 175

nr 1

53-68

In every infinite-dimensional Fréchet space X, we construct a linear subspace E such that E is an $F_{σδσ}$-subset of X and contains a retract R so that $R × E^{ω}$ is not homeomorphic to $E^{ω}$. This shows that Toruńczyk's Factor Theorem fails in the Borel case.

Selections and near-selections in metric linear spaces without local convexity

63%

Dobrowolski T. , van Mill J.

nr 3

215-232

We characterize the AR property in convex subsets of metric linear spaces in terms of certain near-selections.

Topological type of weakly closed subgroups in Banach spaces

51%

Dobrowolski T. , Grabowski J. , Kawamura K.

nr 1

49-62

The main result says that nondiscrete, weakly closed, containing no nontrivial linear subspaces, additive subgroups in separable reflexive Banach spaces are homeomorphic to the complete Erdős space. Two examples of such subgroups in $ℓ^1$ which are interesting from the Banach space theory point of view are discussed.