Tell me more ×  Can you give an example of a complete metric
vector space of uniformly continuous functions that is strictly
contained between the set of uniformly continuous functions on
$\mathbb R^d$ and the Hölder spaces on $\mathbb R^d$?
share|improve this question Can you replace the function
$|\cdot|^\alpha$ in the definition of Holder spaces by another
function? –  timur Sep 11 '11 at 22:46 The phrasing of the
question makes it sound unfortunately like something from an
assignment. You might get more detailed responses if you gave
more information about how you ran into this question, and gave
some motivation (but also see the FAQ concerning what questions
should be asked here and how best to formulate them) –  Captain
Oates Sep 12 '11 at 1:19 What do you mean by containment in this
case? Contained as sets of functions? Must there be some kind of
isometric vector space embedding-type relationship? If so, what
are the topologies on each of the spaces? –  Peter Luthy Sep 12
'11 at 7:38 Thank you for the