Artikel
Lizenziert
Nicht lizenziert
Erfordert eine Authentifizierung
Arcwise Connected Continua and Whitney Maps
-
Ivan Lončar
Veröffentlicht/Copyright:
10. März 2010
Abstract
Let 𝑋 be a non-metric continuum, and 𝐶(𝑋) be the hyperspace of subcontinua of 𝑋. It is known that there is no Whitney map on the hyperspace 2𝑋 for non-metric Hausdorff compact spaces 𝑋. On the other hand, there exist non-metric continua which admit and ones which do not admit a Whitney map for 𝐶(𝑋). In particular, a locally connected or a rimmetrizable continuum 𝑋 admits a Whitney map for 𝐶(𝑋) if and only if it is metrizable. In this paper we investigate the properties of continua 𝑋 which admit a Whitney map for 𝐶(𝑋) or for 𝐶2(𝑋).
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
© Heldermann Verlag
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Artikel in diesem Heft
- 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 𝑛-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 𝐿𝑝
- 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
Schlagwörter für diesen Artikel
Arcwise connected continuum;
hyperspace;
inverse system;
property of Kelley;
smootness;
Whitney map
Artikel in diesem Heft
- 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 𝑛-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 𝐿𝑝
- 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
