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» K -Trivial Closed Sets and Continuous Functions
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JSYML
2000
76views more  JSYML 2000»
13 years 11 months ago
Located Sets and Reverse Mathematics
Let X be a compact metric space. A closed set K X is located if the distance function d(x, K) exists as a continuous realvalued function on X; weakly located if the predicate d(x,...
Mariagnese Giusto, Stephen G. Simpson
JUCS
2008
140views more  JUCS 2008»
13 years 11 months ago
The Computable Multi-Functions on Multi-represented Sets are Closed under Programming
: In the representation approach to computable analysis (TTE) [Grz55, i00], abstract data like rational numbers, real numbers, compact sets or continuous real functions are represe...
Klaus Weihrauch
RC
2006
69views more  RC 2006»
13 years 11 months ago
The Set of Hausdorff Continuous Functions - The Largest Linear Space of Interval Functions
Hausdorff continuous (H-continuous) functions are special interval-valued functions which are commonly used in practice, e.g. histograms are such functions. However, in order to av...
Roumen Anguelov, Svetoslav Markov, Blagovest Sendo...
FOCS
2010
IEEE
13 years 9 months ago
Stability Yields a PTAS for k-Median and k-Means Clustering
We consider k-median clustering in finite metric spaces and k-means clustering in Euclidean spaces, in the setting where k is part of the input (not a constant). For the k-means pr...
Pranjal Awasthi, Avrim Blum, Or Sheffet
JAT
2011
93views more  JAT 2011»
13 years 6 months ago
Approximation theorems for group valued functions
Stone-Weierstrass-type theorems for groups of group-valued functions with discrete range or discrete domain are obtained. We study criteria for a subgroup of the group of continuou...
Jorge Galindo, Manuel Sanchis