Geodesic
Extension of functions preserving the modulus of continuity
Matematičeskie zametki, Tome 61 (1997) no. 2, pp. 236-245

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The problem of the extension of a real-valued function from a subset of a metric space to the entire space is treated. An extension operator preserving the modulus of continuity of a function is proposed and its properties are studied. An application to the problem of the trace of a locally Lipschitz function on a compact subset of a metric space is given. 
@article{MZM_1997_61_2_a4,
     author = {V. A. Milman},
     title = {Extension of functions preserving the modulus of continuity},
     journal = {Matemati\v{c}eskie zametki},
     pages = {236--245},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a4/}
}
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V. A. Milman. Extension of functions preserving the modulus of continuity. Matematičeskie zametki, Tome 61 (1997) no. 2, pp. 236-245. http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a4/