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1
Content available remote

On countable dense and strong n-homogeneity

100%
van Mill J.
Fundamenta Mathematicae
|
2011
|
tom 214
|
nr 3
215-239
EN
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.
2
Content available remote

On Countable Dense and Strong Local Homogeneity

100%
van Mill J.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2005
|
tom 53
|
nr 4
401-408
EN
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.
3
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A countable dense homogeneous space with a dense rigid open subspace

100%
van Mill J.
Fundamenta Mathematicae
|
2008
|
tom 201
|
nr 1
91-98
EN
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.
4
Content available remote

Dimensionsgrad for locally connected Polish spaces

64%
Fedorchuk V. V., van Mill J.
Fundamenta Mathematicae
|
2000
|
tom 163
|
nr 1
77-82
EN
It is shown that for every n ≥ 2 there exists an n-dimensional locally connected Polish space with Dimensionsgrad 1.
5
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Hyperspaces of Peano continua of euclidean spaces

64%
Gladdines H., van Mill J.
Fundamenta Mathematicae
|
1993
|
tom 142
|
nr 2
173-188
EN
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 $L(ℝ^n)$ is homeomorphic to $B^∞$, where B denotes the pseudo-boundary of the Hilbert cube Q.
6
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Selections and near-selections in metric linear spaces without local convexity

64%
Dobrowolski T., van Mill J.
Fundamenta Mathematicae
|
2006
|
tom 192
|
nr 3
215-232
EN
We characterize the AR property in convex subsets of metric linear spaces in terms of certain near-selections.
7
Content available remote

On the Separation Dimension of $K_ω$

64%
Hattori Y., van Mill J.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2013
|
tom 61
|
nr 1
67-70
EN
We prove that $trt K_ω > ω+1$, where trt stands for the transfinite extension of Steinke's separation dimension. This answers a question of Chatyrko and Hattori.
8
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Measures on Corson compact spaces

64%
Kunen K., van Mill J.
Fundamenta Mathematicae
|
1995
|
tom 147
|
nr 1
61-72
EN
We prove that the statement: "there is a Corson compact space with a non-separable Radon measure" is equivalent to a number of natural statements in set theory.
9
Content available remote

Extending monotone mappings

64%
Dijkstra J. J., van Mill J.
Colloquium Mathematicum
|
1998
|
tom 77
|
nr 2
201-210
10
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Equality of the Lebesgue and the inductive dimension functions for compact spaces with a uniform convexity

63%
van Mill J., van de Vel M.
Colloquium Mathematicum
|
1985-1986
|
tom 50
|
nr 2
187-200
11
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Hausdorff measures and two point set extensions

52%
Dijkstra J. J., Kunen K., van Mill J.
Fundamenta Mathematicae
|
1998
|
tom 157
|
nr 1
43-60
EN
We investigate the following question: under which conditions is a σ-compact partial two point set contained in a two point set? We show that no reasonable measure or capacity (when applied to the set itself) can provide a sufficient condition for a compact partial two point set to be extendable to a two point set. On the other hand, we prove that under Martin's Axiom any σ-compact partial two point set such that its square has Hausdorff 1-measure zero is extendable.
12
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Selections that characterize topological completeness

52%
van Mill J., Pelant J., Pol R.
Fundamenta Mathematicae
|
1996
|
tom 149
|
nr 2
127-141
EN
We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].
13
Content available remote

Countable dense homogeneity and λ-sets

52%
Hernández-Gutiérrez R., Hrušák M., van Mill J.
Fundamenta Mathematicae
|
2014
|
tom 226
|
nr 2
157-172
EN
We show that all sufficiently nice λ-sets are countable dense homogeneous (𝖢𝖣𝖧). From this fact we conclude that for every uncountable cardinal κ ≤ 𝔟 there is a countable dense homogeneous metric space of size κ. Moreover, the existence of a meager in itself countable dense homogeneous metric space of size κ is equivalent to the existence of a λ-set of size κ. On the other hand, it is consistent with the continuum arbitrarily large that every 𝖢𝖣𝖧 metric space has size either ω₁ or 𝔠. An example of a Baire 𝖢𝖣𝖧 metric space which is not completely metrizable is presented. Finally, answering a question of Arhangel'skii and van Mill we show that that there is a compact non-metrizable 𝖢𝖣𝖧 space in ZFC.
14
Content available remote

Fake topological Hilbert spaces and characterizations of dimension in terms of negligibility

51%
Dijkstra J., van Mill J.
Fundamenta Mathematicae
|
1985
|
tom 125
|
nr 2
143-153
15
Content available remote

Orderability form selections: Another solution to the orderability problem

51%
van Mill J., Wattel E.
Fundamenta Mathematicae
|
1984
|
tom 121
|
nr 3
219-229
16
Content available remote

Borel sets in compact spaces: some Hurewicz type theorems

51%
van Engelen F., van Mill J.
Fundamenta Mathematicae
|
1984
|
tom 124
|
nr 3
270-286
17
Content available remote

Zero-dimensional countable dense unions of Z-sets in the Hilbert cube

51%
Curtis D. W., van Mill J.
Fundamenta Mathematicae
|
1983
|
tom 118
|
nr 2
103-108
18
Content available remote

The superextension of the closed unit interval is homeomorphic to the Hilbert cube

51%
van Mill J.
Fundamenta Mathematicae
|
1979
|
tom 103
|
nr 3
151-175
19
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

An infinite-dimensional pre-Hilbert space all bounded linear operators of which are simple

51%
van Mill J.
Colloquium Mathematicum
|
1987
|
tom 54
|
nr 1
29-37
20
Content available remote

Les hyperespaces des rétractes absolus et des rétractes absolus de voisinage du plan

45%
Cauty R., Dobrowolski T., Gladdines H., van Mill J.
Fundamenta Mathematicae
|
1995
|
tom 148
|
nr 3
257-282
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