On shape and fundamental deformation retracts II
Theory of equidistance and betweenness relations in regular metric spaces
Concerning the Whitehead Theorem for movable compacta
ANR-spaces which are deformation retracts of some polyhedra
On the homotopy classification of spaces
Various approaches to the fundamental groups
Concerning the shape groups of compact metric spaces
The Whitehead Theorem in the theory of shapes
Uniformly movable compact spaces and their algebraic properties
On shape and fundamental deformation retracts
On rigid subsets of some manifolds
On the geometry of convex sets.
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Various categorical approaches to statistical spaces
CONTENTSIntroduction..............................................................................................................51. Preliminaries........................................................................................................61.0. Measurable, probabilistic, and statistical spaces..............................................61.1. Transition functions..........................................................................................61.2. Linear space of P-bounded...
On metric products
Optimal isometries for a pair of compact convex subsets of ℝⁿ
In 1989 R. Arnold proved that for every pair (A,B) of compact convex subsets of ℝ there is an Euclidean isometry optimal with respect to L₂ metric and if f₀ is such an isometry, then the Steiner points of f₀(A) and B coincide. In the present paper we solve related problems for metrics topologically equivalent to the Hausdorff metric, in particular for metrics for all p ≥ 2 and the symmetric difference metric.
Concerning Sets of the First Baire Category with Respect to Different Metrics
We prove that if and δ are the Hausdorff metric and the radial metric on the space ⁿ of star bodies in ℝ, with 0 in the kernel and with radial function positive and continuous, then a family ⊂ ⁿ that is meager with respect to need not be meager with respect to δ. Further, we show that both the family of fractal star bodies and its complement are dense in ⁿ with respect to δ.
Fractal star bodies
In 1989 R. Arnold proved that for every pair (A,B) of compact convex subsets of ℝ there is an Euclidean isometry optimal with respect to L₂ metric and if f₀ is such an isometry, then the Steiner points of f₀(A) and B coincide. In the present paper we solve related problems for metrics topologically equivalent to the Hausdorff metric, in particular for metrics for all p ≥ 2 and the symmetric difference metric.
Concerning basic notions of the measurement theory
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