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1
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The geometry of laminations

100%
Fokkink R. J., Oversteegen L. G.
Fundamenta Mathematicae
|
1996
|
tom 151
|
nr 3
195-207
EN
A lamination is a continuum which locally is the product of a Cantor set and an arc. We investigate the topological structure and embedding properties of laminations. We prove that a nondegenerate lamination cannot be tree-like and that a planar lamination has at least four complementary domains. Furthermore, a lamination in the plane can be obtained by a lakes of Wada construction.
2
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A hereditarily indecomposable, hereditarily non-chainable planar tree-like continuum

100%
Mohler L., Oversteegen L. G.
Fundamenta Mathematicae
|
1984
|
tom 122
|
nr 3
237-246
3
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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The Menger curve Characterization and extension of homeomorphisms of non-locally-separating closed subsets

89%
Mayer J. C., Oversteegen L. G., Tymchatyn E. D.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 1. Introduction.................................................................................................................................................5 2. Partitioning Peano continua......................................................................................................................10 3. Peano continua and cross-connectedness...............................................................................................18 4. The characterization of the Menger curve.................................................................................................28 5. Extension of homeomorphisms on non-locally-separating, closed subsets of the Menger curve..............34 6. Universality and map extension theorems.................................................................................................42 7. Bibliography..............................................................................................................................................45
4
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On homogeneous totally disconnected 1-dimensional spaces

81%
Kawamura K., Oversteegen L. G., Tymchatyn E. D.
Fundamenta Mathematicae
|
1996
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tom 150
|
nr 2
97-112
EN
The Cantor set and the set of irrational numbers are examples of 0-dimensional, totally disconnected, homogeneous spaces which admit elegant characterizations and which play a crucial role in analysis and dynamical systems. In this paper we will start the study of 1-dimensional, totally disconnected, homogeneous spaces. We will provide a characterization of such spaces and use it to show that many examples of such spaces which exist in the literature in various fields are all homeomorphic. In particular, we will show that the set of endpoints of the universal separable ℝ-tree, the set of endpoints of the Julia set of the exponential map, the set of points in Hilbert space all of whose coordinates are irrational and the set of endpoints of the Lelek fan are all homeomorphic. Moreover, we show that these spaces satisfy a topological scaling property: all non-empty open subsets and all complements of σ-compact subsets are homeomorphic.
5
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On hereditarily decomposable hereditarily equivalent non-metric continua

80%
Mohler L., Oversteegen L. G.
Fundamenta Mathematicae
|
1990
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tom 136
|
nr 1
1-12
6
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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On the structure of tranches in continuously irreducible continua

80%
Mohler L., Oversteegen L. G.
Colloquium Mathematicum
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1987
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tom 54
|
nr 1
23-28
7
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On span and weakly chainable continua

70%
Oversteegen L. G., Tymchatyn E. D.
Fundamenta Mathematicae
|
1984
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tom 122
|
nr 2
159-174
8
Content available remote

On span and chainable continua

70%
Oversteegen L. G., Tymchatyn E. D.
Fundamenta Mathematicae
|
1984
|
tom 123
|
nr 2
137-149
9
Content available remote

On the span of weakly-chainable continua

70%
Oversteegen L. G., Tymchatyn E. D.
Fundamenta Mathematicae
|
1983
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tom 119
|
nr 2
151-156
10
Content available remote

Reduction and irreducibility for words and tree-words

70%
Mohler L., Oversteegen L. G.
Fundamenta Mathematicae
|
1985-1986
|
tom 126
|
nr 2
107-121
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