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Arcwise Connected Continua and Whitney Maps
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Ivan LonΔar
Published/Copyright:
March 10, 2010
Abstract
Let π be a non-metric continuum, and πΆ(π) be the hyperspace of subcontinua of π. It is known that there is no Whitney map on the hyperspace 2π for non-metric Hausdorff compact spaces π. On the other hand, there exist non-metric continua which admit and ones which do not admit a Whitney map for πΆ(π). In particular, a locally connected or a rimmetrizable continuum π admits a Whitney map for πΆ(π) if and only if it is metrizable. In this paper we investigate the properties of continua π which admit a Whitney map for πΆ(π) or for πΆ2(π).
Key words and phrases:: Arcwise connected continuum; hyperspace; inverse system; property of Kelley; smootness; Whitney map
Received: 2003-12-04
Revised: 2005-02-03
Published Online: 2010-03-10
Published in Print: 2005-June
Β© Heldermann Verlag
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- Boundedness for Multilinear Singular Integral Operators on Some Hardy and Herz Type Spaces
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- Some Remarks Concerning Jones Eigenfrequencies and Jones Modes
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Keywords for this article
Arcwise connected continuum;
hyperspace;
inverse system;
property of Kelley;
smootness;
Whitney map
Articles in the same Issue
- Quadric Hypersurfaces Containing a Projectively Normal Curve
- Gelfand Pairs and Generalized d'Alembert's and Cauchy's Functional Equations
- Some Approximation Properties for Modified Baskakov Type Operators
- On a Boundary Value Problem for π-th Order Linear Functional Differential Systems
- Functional Differential Inequalities with Unbounded Delay
- On Absolutely Negligible Sets in Uncountable Solvable Groups
- Disturbance Due to a Time Harmonic Source in Orthotropic Micropolar Viscoelastic Medium
- Semi-Slant Submanifolds of a Locally Product Manifold
- Boundary Regularity for Capillary Surfaces
- Boundedness for Multilinear Singular Integral Operators on Some Hardy and Herz Type Spaces
- Arcwise Connected Continua and Whitney Maps
- On the Fourier Multipliers of the Space πΏπ
- Some Remarks Concerning Jones Eigenfrequencies and Jones Modes
- On the Strong Differentiation of Multiple Integrals along Different Frames
- On the Asymptotic Behaviour of Solutions of Third Order Delay Differential Equations
- Mapping Properties of Integral Operators of Levy Type
