@MISC{CKSPACE1.MIZ,
  AUTHOR = {Kanazashi, Katuhiko and Okazaki, Hiroyuki and Shidama, Yasunari},
  TITLE = {The $C^k$ Space},
  SECTION1 = {Definition of Continuously Differentiable Functions and Some Properties},
  SECTION2 = {Definition of the $C^k$ Space},
  DAY = {9},
  MONTH = {November},
  YEAR = {2012},
  ADDRESS1 = {Shizuoka City},
  ADDRESS2 = {Shinshu University},
  ADDRESS3 = {Shinshu University},
  SUMMARY = {In this article, we formalize continuous differentiability
  of real-valued functions on $n$-dimensional real normed linear spaces.
  Next, we give a definition of the $C^k$ space according
  to \cite{Kosaku:1996}.},
  ACKNOWLEDGMENT = {This work was supported by JSPS KAKENHI 22300285.}}

@BOOK{Kosaku:1996,
 AUTHOR={Yosida, Kosaku},
 TITLE={Functional Analysis (Classics in Mathematics S.)},
 PUBLISHER={Springer},
 YEAR=1996}
