On continuous extension of uniformly continuous functions and metrics
T. Banakh ; N. Brodskiy ; I. Stasyuk ; E. D. Tymchatyn
Colloquium Mathematicae, Tome 116 (2009), p. 191-202 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We prove that there exists a continuous regular, positive homogeneous extension operator for the family of all uniformly continuous bounded real-valued functions whose domains are closed subsets of a bounded metric space (X,d). In particular, this operator preserves Lipschitz functions. A similar result is obtained for partial metrics and ultrametrics.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:284328 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm116-2-4,
     author = {T. Banakh and N. Brodskiy and I. Stasyuk and E. D. Tymchatyn},
     title = {On continuous extension of uniformly continuous functions and metrics},
     journal = {Colloquium Mathematicae},
     volume = {116},
     year = {2009},
     pages = {191-202},
     zbl = {1172.54010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm116-2-4}
}

T. Banakh; N. Brodskiy; I. Stasyuk; E. D. Tymchatyn. On continuous extension of uniformly continuous functions and metrics. Colloquium Mathematicae, Tome 116 (2009) pp. 191-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm116-2-4/