}
Importantly, changing the set
U
{\displaystyle U}
to a different open subset
U
{\displaystyle U’}
(with
K
U
{\displaystyle K\subseteq U’}
) will change the set
C
k
(
K
)
{\displaystyle C^{k}(K)}
from
C
k
(
K
;
U
)
navigate here {\displaystyle C^{k}(K;U)}
to
C
k
(
K
;
U
)
,
{\displaystyle C^{k}(K;U’),}
note 3 so that elements of
C
k
(
go to this website K
)
{\displaystyle C^{k}(K)}
will be functions with domain
U
{\displaystyle U’}
instead of
U
. .