Cone Characterization of the Hilbert Cube. Toruńczyk's Approximation Theorem and Applications. If X is a topological space, then we let H(X) denote the group of autohomeomorphisms of X equipped.
Cell-Like Maps and Fine Homotopy Equivalences. On Homeomorphism Groups and the Compact-Open Topology. Hilbert Space is Homeomorphic to the Countable Infinite Product of Lines. The Estimated Homeomorphism Extension Theorem. The Estimated Homeomorphism Extension Theorem for Compacta in s. Constructing New Homeomorphisms from Old. An Introduction to Infinite-Dimensional Topology. Gerald Beer hasproved that the hyperspaceC(X) is Atsuji whenXis either compactor uniformly discrete. Characterization of Finite-Dimensional ANR's and AR's. 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. Various Kinds of Infinite-Dimensionality.ĥ. The Inductive Dimension Functions ind and Ind. The Brouwer Fixed-Point Theorem and Applications. The Michael Selection Theorem and Applications. In the process of proving this result several interesting and useful detours are made. The text is self-contained for readers with a modest knowledge of general topology and linear algebra the necessary background material is collected in chapter 1, or developed as needed.One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds. Chapter 6 is an introduction to infinite-dimensional topology it uses for the most part geometric methods, and gets to spectacular results fairly quickly. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. 154 (2007), 1002–1007.The first part of this book is a text for graduate courses in topology. Pellicer–Covarrubias, Cells in hyperspaces, Topology Appl. Pellicer, The hyperspaces C ( p, X ), Topol. Vershik Journal of Mathematical Sciences, Vol. Nadler, Jr., Continuum Theory: An introduction, Monographs and Textbooks in Pure and Applied Mathematics, 158, Marcel Dekker, Inc., New York and Basel, 1992. Adic realizations of ergodic actions by homeomorphisms of Markov compacta and ordered Bratteli diagrams A. 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. 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. 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. 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. The authors wish to thank Eli Vanney Roblero and Rosemberg Toalá for the fruitful discussions.
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