Geodesic
On continuous extension of uniformly continuous functions and metrics
T. Banakh 1   ; N. Brodskiy 2   ; I. Stasyuk 1   ; E. D. Tymchatyn 3
1 Department of Mechanics and Mathematics Lviv National University Universytetska St. 1 79000 Lviv, Ukraine
2 Department of Mathematics The University of Tennessee 104 Aconda Court 1534 Cumberland Avenue Knoxville, TN 37996-0612, U.S.A.
3 Department of Mathematics and Statistics University of Saskatchewan McLean Hall, 106 Wiggins Road Saskatoon, SK S7N 5E6, Canada
Colloquium Mathematicum, Tome 116 (2009) no. 2, pp. 191-202 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm116-2-4
Keywords: prove there exists continuous regular positive homogeneous extension operator family uniformly continuous bounded real valued functions whose domains closed subsets bounded metric space particular operator preserves lipschitz functions similar result obtained partial metrics ultrametrics

T. Banakh  1   ; N. Brodskiy  2   ; I. Stasyuk  1   ; E. D. Tymchatyn  3

1 Department of Mechanics and Mathematics Lviv National University Universytetska St. 1 79000 Lviv, Ukraine
2 Department of Mathematics The University of Tennessee 104 Aconda Court 1534 Cumberland Avenue Knoxville, TN 37996-0612, U.S.A.
3 Department of Mathematics and Statistics University of Saskatchewan McLean Hall, 106 Wiggins Road Saskatoon, SK S7N 5E6, Canada 
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T. Banakh; N. Brodskiy; I. Stasyuk; E. D. Tymchatyn. On continuous extension of uniformly continuous
 functions and metrics. Colloquium Mathematicum, Tome 116 (2009) no. 2, pp. 191-202. doi: 10.4064/cm116-2-4

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