489 research outputs found
Topological entropy and a theorem of Misiurewicz, Szlenk and Young(General and Geometric Topology and Geometric Group Theory)
Function spaces and isometrical extensions of bounded isometries of separable metric spaces (The present situation of set-theoretic and geometric topology and its prospects)
On the property of kelley in the hyperspace and Whitney continua
AbstractIn this paper, we introduce the notion of property [K]∗ which implies property [K], and we show the following: Let X be a continuum and let ω be any Whitney map for C(X). Then the following are equivalent. (1) X has property [K]∗. (2) C(X) has property [K]∗. (3) The Whitney continuum ω−1(t) (0⩽t<ω(X)) has property [K]∗.As a corollary, we obtain that if a continuum X has property [K]∗, then C(X) has property [K] and each Whitney continuum in C(X) has property [K]. These are partial answers to Nadler's question and Wardle's question ([10, (16.37)] and [11, p. 295]).Also, we show that if each continuum Xn (n=1,2,3,…) has property [K]∗, then the product ∏Xn has property [K]∗, hence C(∏Xn) and each Whitney continuum have property [K]∗. It is known that there exists a curve X such that X has property [K], but X×X does not have property [K] (see [11])
TOPOLOGICAL ENTROPY AND TOPOLOGICAL STRUCTURES OF CONTINUA (Research Trends on Set-theoretic and Geometric Topology and their cooperation with various branches)
RECONSTRUCTIONS OF ONE-SIDED DYNAMICAL SYSTEMS FROM THE ANALYSIS OF EXPERIMENTAL TIME SERIES (Recent Progress in General Topology and its Related Fields)
On dynamical systems of finite-dimensional compact metric spaces and finite-to-one zero-dimensional covers (Set-Theoretic and Geometric Topology, and their applications to related fields)
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