The set of exponents for isomorphic extensions of Hölder maps is not always closed.
Extracta mathematicae, Tome 23 (2008) no. 2.

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     author = {Delpech,  S. },
     title = {The set of exponents for isomorphic extensions of {H\"older} maps is not always closed.},
     journal = {Extracta mathematicae},
     pages = {131-137},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EXMATH_2008_2008_1_a10/}
}
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Delpech,  S. . The set of exponents for isomorphic extensions of Hölder maps is not always closed.. Extracta mathematicae, Tome 23 (2008) no. 2. http://geodesic.mathdoc.fr/item/EXMATH_2008_2008_1_a10/