Representing Countable Groups by Homeomorphism Groups in Hilbert Space.
Inductive čech completeness and dimension
Homogeneous subsets of the real line
Relations between ß X / X and a Certain Subspace of ... X.
The superextension of the closed unit interval is homeomorphic to the Hilbert cube
Superextensions of metrizable continua are Hilbert cubes
A uniquely homogeneous space need not be a topological group
Characterization of a certain subset of the Cantor set
A boundary set for the Hilbert cube containing no arcs
An infinite-dimensional pre-Hilbert space all bounded linear operators of which are simple
On countable dense and strong n-homogeneity
We prove that if a space X is countable dense homogeneous and no set of size n-1 separates it, then X is strongly n-homogeneous. Our main result is the construction of an example of a Polish space X that is strongly n-homogeneous for every n, but not countable dense homogeneous.
On nowhere first-countable compact spaces with countable -weight
The minimum weight of a nowhere first-countable compact space of countable -weight is shown to be , the least cardinal for which the real line can be covered by many nowhere dense sets.
A countable dense homogeneous space with a dense rigid open subspace
We show that there is a Polish space which is countable dense homogeneous but contains a dense open rigid connected subset. This answers several questions of Fitzpatrick and Zhou.
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.
Totally divergent dense sets in Cantor cubes
Hyperspaces of infinite-dimensional compacta
Extending monotone mappings
The compactness number of a compact topological space I
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.
Fake topological Hilbert spaces and characterizations of dimension in terms of negligibility
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