@MISC{C0SP3.MIZ,
  AUTHOR = {Yamazaki, Hiroshi and Miyajima, Keiichi and Shidama, Yasunari},
  TITLE = {Functional Space Consisted by Continuous Functions on Topological Space},
  SECTION1 = {Real Vector Space of Continuous Functions},
  SECTION2 = {Real Vector Space of Continuous Functions (Norm Space Version)},
  SECTION3 = {Normed Topological Linear Space},
  SECTION4 = {Real Norm Space of Continuous Functions},
  SECTION5 = {Some Properties of Support},
  SECTION6 = {Space of Real-valued Continuous Functionals with Bounded Support},
  DAY = {30},
  MONTH = {March},
  YEAR = {2021},
  ADDRESS1 = {Nagano Prefectural Institute of Technology\\Nagano, Japan},
  ADDRESS2 = {Ibaraki University \\Ibaraki, Japan},
  ADDRESS3 = {Karuizawa Hotch 244-1\\Nagano, Japan},
  MSC2010 = {46E10},
  KEYWORDS = {continuous function space; compact topological space; Banach space},
  SUMMARY = {In this article, first we give a definition of a functional space
     which is constructed from all continuous functions defined on
     a compact topological space.
     We prove that this functional space is a Banach space.
     Next, we give a definition of a function space which is constructed
     from all continuous functions with bounded support.
     We also prove that this function space is a normed space.},
  ACKNOWLEDGEMENT = {This work was supported by JSPS KAKENHI Grant Numbers
    JP17K00182.}}


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@BOOK{Schwartz1997b,
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  AUTHOR = {Laurent Schwartz},
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  MONTH = {10}}

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