Knaster's problem for almost (Zp)k(Z_p)^k-orbits

In this paper some new cases of Knaster's problem on continuous maps from spheres are established. In particular, we consider an almost orbit of a $p$-torus $X$ on the sphere, a continuous map $f$ from the sphere to the real line or real plane, and show that $X$ can be rotated so that $f$ becomes constant on $X$

A topological central point theorem

In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.Comment: In this version some typos were corrected after the official publicatio

Borsuk-Ulam type theorems for G-spaces with applications to Tucker type lemmas

In this paper we consider several generalizations of the Borsuk-Ulam theorem for G-spaces and apply these results to Tucker type lemmas for G-simplicial complexes and PL-manifolds.Comment: 20 page

Borsuk–Ulam type theorems for G-spaces with applications to Tucker type lemmas

In this paper we consider several generalizations of the Borsuk–Ulam theorem for G-spaces and apply these results to Tucker type lemmas for G-simplicial complexes and PL-manifolds

Configuration-like spaces and coincidences of maps on orbits

In this paper we study the spaces of $q$-tuples of points in a Euclidean space, without $k$-wise coincidences (configuration-like spaces). A transitive group action by permuting these points is considered, and some new upper bounds on the genus (in the sense of Krasnosel'skii--Schwarz and Clapp--Puppe) for this action are given. Some theorems of Cohen--Lusk type for coincidence points of continuous maps to Euclidean spaces are deduced

Waist of the sphere for maps to manifolds

We generalize the sphere waist theorem of Gromov and the Borsuk--Ulam type measure partition lemma of Gromov--Memarian for maps to manifolds

Tverberg-type theorems for intersecting by rays

In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set

Analogues of the central point theorem for families with dd-intersection property in Rd\mathbb R^d

In this paper we consider families of compact convex sets in $\mathbb R^d$ such that any subfamily of size at most $d$ has a nonempty intersection. We prove some analogues of the central point theorem and Tverberg's theorem for such families