scholarly journals Continuous selections of Lipschitz extensions in metric spaces

2015 ◽  
Vol 28 (3) ◽  
pp. 741-759 ◽  
Author(s):  
Rafa Espínola ◽  
Adriana Nicolae
Keyword(s):  
Metric Spaces ◽  
Continuous Selections ◽  
Lipschitz Extensions

scholarly journals Lipschitz Extensions to Finitely Many Points

2018 ◽  
Vol 6 (1) ◽  
pp. 174-191 ◽  
Author(s):  
Giuliano Basso
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Metric Spaces ◽  
Lipschitz Constant ◽  
Target Space ◽  
Square Root ◽  
Lipschitz Maps ◽  
Lipschitz Map ◽  
Lipschitz Extensions

AbstractWe consider Lipschitz maps with values in quasi-metric spaces and extend such maps to finitely many points. We prove that in this context every 1-Lipschitz map admits an extension such that its Lipschitz constant is bounded from above by the number of added points plus one. Moreover, we prove that if the source space is a Hilbert space and the target space is a Banach space, then there exists an extension such that its Lipschitz constant is bounded from above by the square root of the total of added points plus one. We discuss applications to metric transforms.

scholarly journals Lipschitz extensions and Lipschitz retractions in metric spaces

1981 ◽  
Vol 45 (2) ◽  
pp. 245-250 ◽  
Author(s):  
Nguyen Van Khue ◽  
Nguyen To Nhu
Keyword(s):  
Metric Spaces ◽  
Lipschitz Extensions

scholarly journals Optimal Lipschitz extensions

2018 ◽  
Vol 20 ◽  
pp. 02010
Author(s):  
Thanh Viet Phan
Keyword(s):  
Lipschitz Function ◽  
Metric Spaces ◽  
Lipschitz Constant ◽  
Extension Problem ◽  
Lipschitz Extension ◽  
Open Questions ◽  
Lipschitz Extensions

The classical Lipschitz extension problem in concerned for conditions on a pair of metric spaces (X,dX) and (Y,dY) such that for all Ω ⊂ X and for all Lipschitz function and for all Lipschitz function f : Ω → Y, then there is a function g : X → Y that extends f and has the same Lipschitz constant as f . In this paper we discuss some results and open questions related to that issue.

Crystallography in two-dimensional metric spaces*

1969 ◽  
Vol 130 (1-6) ◽  
pp. 277-303 ◽  
Author(s):  
Aloysio Janner ◽  
Edgar Ascher
Keyword(s):  
Metric Spaces ◽  
Two Dimensional
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