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A free group of piecewise linear transformations

100%

Tomkowicz G.

Colloquium Mathematicum

2011

tom 125

nr 2

141-146

We prove the following conjecture of J. Mycielski: There exists a free nonabelian group of piecewise linear, orientation and area preserving transformations which acts on the punctured disk {(x,y) ∈ ℝ²: 0 < x² + y² < 1} without fixed points.

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

63%

Mycielski J., Tomkowicz G.

Fundamenta Mathematicae

2013

tom 222

nr 3

289-290

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Fundamenta Mathematicae

2 Tomkowicz G.

1 Mycielski J.

1 2013

1 2011

Wyniki wyszukiwania

A free group of piecewise linear transformations

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