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- Krystyna Trybulec Kuperberg, Wlodzimierz Kuperberg, Jirí Matousek, Pavel Valtr
- Discrete & Computational Geometry
- 1999

Let C be a system (finite or infinite) of centrally symmetric convex bodies in IR with disjoint interiors; we call such a C a packing . For a real number ε > 0 and for C ∈ C, we let C denote C enlarged by the factor 1+ ε from its center, that is, C = (1+ ε)(C − c) + c, where c stands for the center of symmetry C. Let us call the closure of the set C \C the… (More)

Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M . Consider the topological group H(M,D) which consists of all autohomeomorphisms of M that map D onto itself equipped with the compact-open topology. We present a complete solution to the topological classification… (More)

Using the theory of plugs and the self-insertion construction due to the second author, we prove that a foliation of any codimension of any manifold can be modified in a real analytic or piecewise-linear fashion so that all minimal sets have codimension 1. In particular, the 3-sphere S has a real analytic dynamical system such that all limit sets are… (More)

- Andrzej Trybulec, Artur Kornilowicz, Adam Naumowicz, Krystyna Trybulec Kuperberg
- Journal of Automated Reasoning
- 2012

The collection of works for this special issue was inspired by the presentations given at the 2011 AMS Special Session on Formal Mathematics for Mathematicians: Developing Large Repositories of Advanced Mathematics. The issue features a collection of articles by practitioners of formalizing proofs who share a deep interest in making computerized mathematics… (More)

- VIKTOR L. GINZBURG, Krystyna Kuperberg, +4 authors Maria Schonbek
- 1997

We construct a proper C-smooth function on R such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.

It is shown that for every triple of integers (α, β, γ) such that α ≥ 1, β ≥ 1, and γ ≥ 2, there is a homogeneous, non-bihomogeneous continuum whose every point has a neighborhood homeomorphic the Cartesian product of Menger compacta μ ×μ × μ . In particular, there is a homogeneous, non-bihomogeneous, Peano continuum of covering dimension four.

The author constructs a locally connected, homogeneous, finitedimensional, compact, metric space which is not bihomogeneous, thus providing a compact counterexample to a problem posed by B. Knaster around 1921.

If C is a Jordan curve on the plane and P, Q ∈ C, then the segment PQ is called a chord of the curve C. A point inside the curve is called equichordal if every two chords through this point have the same length. Fujiwara in 1916 and independently Blaschke, Rothe and Weitzenböck in 1917 asked whether there exists a curve with two distinct equichordal points… (More)

- AS ORBITS, ROBERT W. GHRIST, Krystyna Kuperberg
- 1995

We construct counterexamples to some conjectures of J. Birman and R. F. Williams concerning the knotting and linking of closed orbits of ows on 3-manifolds. By establishing the existence of \universal templates," we produce examples of ows on S containing closed orbits of all knot and link types simultaneously. In particular, the set of closed orbits of any… (More)

The pseudo-circle is known to be nonhomogeneous. The original proofs of this fact were discovered independently by L. Fearnley [6] and J.T. Rogers, Jr. [17]. The purpose of this paper is to provide an alternative, very short proof based on a result of D. Bellamy and W. Lewis [4].