On the second homotopy group of SC(Z)SC(Z)

In our earlier paper (K. Eda, U. Karimov, and D. Repov\v{s}, \emph{A construction of simply connected noncontractible cell-like two-dimensional Peano continua}, Fund. Math. \textbf{195} (2007), 193--203) we introduced a cone-like space $SC(Z)$. In the present note we establish some new algebraic properties of $SC(Z)$

THE URYSOHN-MENGER SUM FORMULA: AN EXTENSION OF THE DYDAK-WALSH THEOREM TO DIMENSION ONE

Abstract Let X be a finite-dimensional separable metric space, presented as a disjoint union of subsets, X -A U B. We prove the following theorem: For every prime p, c-dim^^ X < c-din^ A + c-diiri2 p B + 1. This improves upon some of the earlier work by Dydak and Walsh. 1991 Mathematics subject classification (Amer. Math. Soc): primary 55M10, 55P20; secondary 54F45, 55P99

Topology and Chaos

Abstract. We discuss some basic topological techniques used in the study of chaotic dynamical systems. This paper is partially motivated by a talk given by the second author at the 7th international summer school and conference Chaos 2008: Let's Face Chaos Through Nonlinear Dynamic