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1
Content available remote

Non-amenable groups with amenable action and some paradoxical decompositions in the plane

100%
Mycielski J.
Colloquium Mathematicum
|
1998
|
tom 75
|
nr 1
149-157
2
Content available remote

On the structure of closed 3-manifolds

100%
Mycielski J.
Fundamenta Mathematicae
|
2003
|
tom 177
|
nr 3
193-208
EN
We will show that for every irreducible closed 3-manifold M, other than the real projective space P³, there exists a piecewise linear map f: S → M where S is a non-orientable closed 2-manifold of Euler characteristic χ ≡ 2 (mod 3) such that $|f^{-1}(x)| ≤ 2$ for all x ∈ M, the closure of the set ${x ∈ M : |f^{-1}(x)| = 2}$ is a cubic graph G such that $S - f^{-1}(G)$ consists of 1/3(2-χ) + 2 simply connected regions, M - f(S) consists of two disjoint open 3-cells such that f(S) is the boundary of each of them, and f has some additional interesting properties. The pair $(S,f^{-1}(G))$ fully determines M, and the minimal value of 1/3(2-χ) is a natural topological invariant of M. Given S there are only finitely many M's for which there exists a map f: S → M with all those properties. Several open problems concerning the relationship between G and M are raised.
3
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Axioms which imply GCH

100%
Mycielski J.
Fundamenta Mathematicae
|
2003
|
tom 176
|
nr 3
193-207
EN
We propose some new set-theoretic axioms which imply the generalized continuum hypothesis, and we discuss some of their consequences.
4
Content available remote

Uniform approximation with linear combinations of reproducing kernels

64%
Mycielski J., Świerczkowski S.
Studia Mathematica
|
1996
|
tom 121
|
nr 2
105-114
EN
We show several theorems on uniform approximation of functions. Each of them is based on the choice of a special reproducing kernel in an appropriate Hilbert space. The theorems have a common generalization whose proof is founded on the idea of the Kaczmarz projection algorithm.
5
Content available remote

On the Kaczmarz algorithm of approximation in infinite-dimensional spaces

64%
Kwapień S., Mycielski J.
Studia Mathematica
|
2001
|
tom 148
|
nr 1
75-86
EN
The Kaczmarz algorithm of successive projections suggests the following concept. A sequence $(e_{k})$ of unit vectors in a Hilbert space is said to be effective if for each vector x in the space the sequence (xₙ) converges to x where (xₙ) is defined inductively: x₀ = 0 and $xₙ = x_{n-1} + αₙeₙ$, where $αₙ = ⟨x - x_{n-1},eₙ⟩$. We prove the effectivity of some sequences in Hilbert spaces. We generalize the concept of effectivity to sequences of vectors in Banach spaces and we prove some results for this more general concept.
6
Content available remote

The prevalence of permutations with infinite cycles

64%
Dougherty R., Mycielski J.
Fundamenta Mathematicae
|
1994
|
tom 144
|
nr 1
89-94
EN
A number of recent papers have been devoted to the study of prevalence, a generalization of the property of being of full Haar measure to topological groups which need not have a Haar measure, and the dual concept of shyness. These concepts give a notion of "largeness" which often differs from the category analogue, comeagerness, and may be closer to the intuitive notion of "almost everywhere." In this paper, we consider the group of permutations of natural numbers. Here, in the sense of category, "almost all" permutations have only finite cycles. In contrast, we show that, in terms of prevalence, "almost all" permutations have infinitely many infinite cycles and only finitely many finite cycles; this set of permutations comprises countably many conjugacy classes, each of which is non-shy.
7
Content available remote

The Banach-Tarski paradox for the hyperbolic plane (II)

64%
Mycielski J., Tomkowicz G.
Fundamenta Mathematicae
|
2013
|
tom 222
|
nr 3
289-290
EN
The second author found a gap in the proof of the main theorem in [J. Mycielski, Fund. Math. 132 (1989), 143-149]. Here we fill that gap and add some remarks about the geometry of the hyperbolic plane ℍ².
8
Content available remote

Erratum to the paper "On the Kaczmarz algorithm of approximation in infinite-dimensional spaces" (Studia Math. 148 (2001), 75-86)

64%
Kwapień S., Mycielski J.
Studia Mathematica
|
2006
|
tom 176
|
nr 1
9
Content available remote

Errata for the paper "Equationally compact algebras II" (Fundamenta Mathematica 61 (1968), pp. 271-281)

64%
Mycielski J., Ryll-Nardzewski C.
Fundamenta Mathematicae
|
1968
|
tom 62
|
nr 3
309
10
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Content available

On the shortest curve which meets all the lines which meet a circle

52%
Faber V., Mycielski J., Pedersen P.
Annales Polonici Mathematici
|
1984
|
tom 44
|
nr 3
249-266
11
Content available remote

Homomorphisms of direct powers of algebras

52%
Ehrenfeucht A., Fajtlowicz S., Mycielski J.
Fundamenta Mathematicae
|
1979
|
tom 103
|
nr 3
189-203
12
Content available remote

Erratum to the paper "The Axion of Choice, the Löwenheim–Skolem Theorem and Borel models" (Fund. Math. 137 (1991), 53-58)

52%
Malitz J., Mycielski J., Reinhardt W. N.
Fundamenta Mathematicae
|
1991-1992
|
tom 140
|
nr 2
197
13
Content available remote

The Axiom of Choice, the Löwenheim-Skolem Theorem and Borel models

52%
Malitz J., Mycielski J., Reinhardt W.
Fundamenta Mathematicae
|
1991
|
tom 137
|
nr 1
53-58
14
Content available remote

Sur un problème du calcul de probabilité (I) (Le mouvement d'une molécule sur une droite)

51%
Mycielski J., Paszkowski S.
Studia Mathematica
|
1955-1956
|
tom 15
|
nr 2
188-200
15
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

An infinite solitaire game with a random strategy

51%
Ehrenfeucht A., Mycielski J.
Colloquium Mathematicum
|
1979
|
tom 42
|
nr 1
115-118
16
Content available remote

Sur les représentations des nombres naturels par des puissances à base et exposant naturels

50%
Mycielski J.
Colloquium Mathematicum
|
1949-1950
|
tom 2
|
nr 3-4
254-260
17
Content available remote

Kazimierz Zarankiewicz (2.V.1902 - 5.IX.1959)

46%
Bergman S., Duda R., Knaster B., Mycielski J., Schinzel A.
Colloquium Mathematicum
|
1964
|
tom 12
|
nr 2
277-288
18
Content available remote

Sur les décompositions d'ensembles connexes

45%
Knaster B., Lelek A., Mycielski J.
Colloquium Mathematicum
|
1958
|
tom 6
|
nr 1
227-246
19
Content available remote

On free groups of motions and decompositions of the Euclidean space

45%
Mycielski J., Świerczkowski S.
Fundamenta Mathematicae
|
1958
|
tom 45
|
nr 1
286-199
20
Content available remote

On the Lebesgue measurability and the axiom of determinateness

45%
Mycielski J., Świerczkowski S.
Fundamenta Mathematicae
|
1964
|
tom 54
|
nr 1
67-71
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