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# Search results

7 records were found.

## On the number of points in a lattice polytope

Comment: two pages

## On some classical constructions extended to hyperbolic geometry

Comment: 12 pages, 6 figures

## Kadets type theorems for partitions of a convex body

For convex partitions of a convex body $B$ we prove that we can put a homothetic copy of $B$ into each set of the partition so that the sum of homothety coefficients is $\ge 1$. In the plane the partition may be arbitrary, while in higher dimensions we need certain restrictions on the partition.

## Inscribing a regular octahedron into polytopes

We prove that any simple polytope (and some non-simple polytopes) in $\mathbb R^3$ admits an inscribed regular octahedron.

## Cutting the same fraction of several measures

Comment: 7 pages 2 figures

## Borsuk-Ulam type theorems for metric spaces

In this paper we study the problems of the following kind: For a pair of topological spaces $X$ and $Y$ find sufficient conditions that under every continuous map $f : X\to Y$ a pair of sufficiently distant points is mapped to a single point.

## The Extremal Spheres Theorem

Comment: 9 pages, 4 figures