![]() ![]() Dugundji, Fixed Point Theory (Springer, New York, 2003). Beer, Topologies on Closed and Closed Convex Sets (Kluwer Academic, Dordrecht, 1993).Ī. Storozhuk, “Topological and geometrical properties of spaces with symmetric and nonsymmetric f-quasimetrics,” Topol. Covering mappings and coincidence points,” Izv.: Math. Greshnov, “( q 1, q 2)-quasimetric spaces. ![]() Nadler, Jr., “Induced universal maps and some hyperspaces with the fixed point property,” Proc. Noussair, “The Schauder–Tychonoff fixed point theorem and applications,” Mat. Antonino, “On Lebesgue quasi-metrizability,” Boll. West, “A note on Lebesgue spaces,” Topol. Beer, “Metric spaces on which continuous functions are uniformly continuous and Hausdorff distance,” Proc. Van Vleck, “The locally finite topology on 2 X,” Proc. Kundu, “Atsuji completions vis-à-vis hyperspaces,” Math. Naimpally, “Distance functionals and suprema of hyperspace topologies,” Ann. Kundu, “Atsuji completions: Equivalent characterisations,” Topol. Beer, “Between compactness and completeness,” Topol. Atsuji, “Uniform continuity of continuous functions of metric spaces,” Pac. Kundu, “More about the cofinally complete spaces and the Atsuji spaces,” Houston J. Krasinkiewicz, On homeomorphisms of the Sierpinski curve, Comment. Beer, “More about metric spaces on which continuous functions are uniformly continuous,” Bull. Pasquale, “A new approach to a hyperspace theory,” J. The Curtis-Schori-West Hyperspace Theorem.R. Vershik Journal of Mathematical Sciences, Vol. Cone Characterization of the Hilbert Cube. Adic realizations of ergodic actions by homeomorphisms of Markov compacta and ordered Bratteli diagrams A. Toruńczyk's Approximation Theorem and Applications. Cell-Like Maps and Fine Homotopy Equivalences. 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. of non-refinable mappings whose induced mappings are near-homeomorphisms, in. Constructing New Homeomorphisms from Old. For a metric continuum X we denote by 2X and C(X) the hyperspaces of all. An Introduction to Infinite-Dimensional Topology. Characterization of Finite-Dimensional ANR's and AR's. 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. The first part of this book is a text for graduate courses in topology. ![]()
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