On fixed points of maximalizing mappings in posets.
On fixed points of set-valued directional contractions.
On fixed-point theorems in complete metric spaces
On f.p.p. and f.*p.p. of some not locally connected continua
On fractional iterates of a homeomorphism of the plane
We find all continuous iterative roots of nth order of a Sperner homeomorphism of the plane onto itself.
On free topological algebras
On fuzzy -contractive mappings in fuzzy metric spaces.
On game-theoretic methods in the theory of Souslin sets
On generalized games in -spaces
We show that a recent existence result for the Nash equilibria of generalized games with strategy sets in -spaces is false. We prove that it becomes true if we assume, in addition, that the feasible set of the game (the set of all feasible multistrategies) is closed.
On generalized implicit vector equilibrium problems in topological ordered spaces.
On groups of essential values of topological cylinder cocycles over minimal rotations
A theory of essential values of cocycles over minimal rotations with values in locally compact Abelian groups, especially , is developed. Criteria for such a cocycle to be conservative are given. The group of essential values of a cocycle is described.
On Hausdorff dimension of random fractals.
On hereditarily normal topological groups
We investigate hereditarily normal topological groups and their subspaces. We prove that every compact subspace of a hereditarily normal topological group is metrizable. To prove this statement we first show that a hereditarily normal topological group with a non-trivial convergent sequence has -diagonal. This implies, in particular, that every countably compact subspace of a hereditarily normal topological group with a non-trivial convergent sequence is metrizable. Another corollary is that under...
On heredity of strongly proximal actions
We prove that action of a semigroup on compact metric space by continuous selfmaps is strongly proximal if and only if action on is strongly proximal. As a consequence we prove that affine actions on certain compact convex subsets of finite-dimensional vector spaces are strongly proximal if and only if the action is proximal.
On homeomorphic and diffeomorphic solutions of the Abel equation on the plane
We consider the Abel equation φ[f(x)] = φ(x) + a on the plane ℝ², where f is a free mapping (i.e. f is an orientation preserving homeomorphism of the plane onto itself with no fixed points). We find all its homeomorphic and diffeomorphic solutions φ having positive Jacobian. Moreover, we give some conditions which are equivalent to f being conjugate to a translation.
On homogeneous totally disconnected 1-dimensional spaces
The Cantor set and the set of irrational numbers are examples of 0-dimensional, totally disconnected, homogeneous spaces which admit elegant characterizations and which play a crucial role in analysis and dynamical systems. In this paper we will start the study of 1-dimensional, totally disconnected, homogeneous spaces. We will provide a characterization of such spaces and use it to show that many examples of such spaces which exist in the literature in various fields are all homeomorphic. In particular,...
On indecomposability and composants of chaotic continua
A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x,y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that . A homeomorphism f: X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ ℤ such that . Clearly, every expansive homeomorphism is continuum-wise expansive, but the converse assertion is not true. In [6], we defined the notion of chaotic continua of homeomorphisms...
On infinite real trace rational languages of maximum topological complexity.
On injective multivalued semiflows
On internal composants of indecomposable plane continua