![]() Nadler, Jr., Hyperspaces of Sets, Pure and Appl. Lewis, Most maps of the pseudo-arc are homeomorphisms, Proc. Given uniformly homeomorphic metric spacesXandY, itis proved that the hyperspaces C(X) andC(Y) are uniformly home-omorphic, where C(X) denotes the collection of all nonempty closedsubsets of X, and is endowed with Hausdor distance. Lelek, On weakly chainable continua, Fund. ![]() ![]() Kennedy, The construction of chaotic homeomorphisms on chainable continua, Topology Appl. Kelley, Hyperspaces of a continuum, Trans. Kato, Knaster-like chainable continua admit no expansive homeomorphisms, unpublished. Kato, Chaotic continua of (continuum-wise) expansive homeomorphisms and chaos in the sense of Li and Yorke, Fund. According to this result, theM-systems are classified completely: if (X,f) is an M-system, then f satisfies oneof the following four properties exactly, (a) f is equicontinuous (b) f is minimaland weakly mixing (c) f is minimal but neither equicontinuous nor weakly mixing (d) f is non-minimal. Kato, Continuum-wise expansive homeomorphisms, Canad. Kato, Expansive homeomorphisms in continuum theory, Topology Appl. Kato, Expansive homeomorphisms and indecomposability, Fund. Hamilton, A fixed point theorem for the pseudo-arc and certain other metric continua, Proc. Fearnley, Characterizations of the continuous images of the pseudo-arc, Trans. Bing, Concerning hereditarily indecomposable continua, Pacific J. Bing, A homogeneous indecomposable plane continuum, Duke Math. Every uniformly continuous homeomorphism f : X Y between metric spaces lifts to a continuous mapping Ff : H(X) H(Y ) of the corresponding hyperspaces. In particular, this notion is invariant under affine homeomorphism, i.e., if. Pellicer–Covarrubias, Cells in hyperspaces, Topology Appl. Observe that the definition of rint K has been stated in affine topological terms. Search 209,244,544 papers from all fields of science. Writing (X, Y) we always understand that Y is a subspace of X. Skip to search form Skip to main content Skip to account menu. On hyperspacesand homeomorphism groups497 Allmaps considered in thispaper are continuous. Semantic Scholar extracted view of 'Lipschitz homeomorphisms of the Hilbert cube' by J. Pellicer, The hyperspaces C ( p, X ), Topol. Semantic Scholar extracted view of 'Lipschitz homeomorphisms of the Hilbert cube' by J. Nadler, Jr., Continuum Theory: An introduction, Monographs and Textbooks in Pure and Applied Mathematics, 158, Marcel Dekker, Inc., New York and Basel, 1992. Nadler, Jr., Hyperspaces of Sets: A Text with Research Questions, Monographs and Textbooks in Pure and Applied Mathematics, 49, Marcel Dekker, Inc., New York and Basel, 1978. Krasinkiewicz, On homeomorphisms of the Sierpinski curve, Comment. Martínez de la Vega, Dimension of n-fold hyperspaces of graphs, Houston J. Nadler, Jr., Hyperspaces, Fundamentals and recent advances, Monographs and Textbooks in Pure and Applied Mathematics, 216, New York. Hyperspaces of finite subsets of non-separable Hilbert spaces. Eberhart, Intervals of continua which are Hilbert Cubes, Proc. Toalá–Enríquez, Uniqueness of the hyperspaces C ( p, X ) in the class of trees, Topology Appl. on C(x) to homeomorphisms on hyperspaces, Topology Appl. ![]() We also want to thank Professors Fernando Macías Romero and David Herrera Carrasco for asking the questions wich motivated us to write down this paper. algebraic and vertical homeomorphisms on C(x) is dense in H(C(x)) with the. The authors wish to thank Eli Vanney Roblero and Rosemberg Toalá for the fruitful discussions. ![]()
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