On continuous extension of uniformly continuous functions and metrics

• Autorzy: T. Banakh , N. Brodskiy , I. Stasyuk , E. D. Tymchatyn
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54E35: Metric spaces, metrizability
• 54C20: Extension of maps
• 54E40: Special maps on metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 116
• Numer: 2
• Strony: 191-202

Daty

wydano

2009

Twórcy

autor

T. Banakh

• Department of Mechanics and Mathematics, Lviv National University, Universytetska St. 1, 79000 Lviv, Ukraine

autor

N. Brodskiy

• Department of Mathematics, The University of Tennessee, 104 Aconda Court, 1534 Cumberland Avenue, Knoxville, TN 37996-0612, U.S.A.

autor

I. Stasyuk

• Department of Mechanics and Mathematics, Lviv National University, Universytetska St. 1, 79000 Lviv, Ukraine

autor

E. D. Tymchatyn

• Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, SK S7N 5E6, Canada

Identyfikatory

DOI

10.4064/cm116-2-4