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2013 | 21 | 1 | 25-31
Tytuł artykułu

The CkSpace

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article, we formalize continuous differentiability of realvalued functions on n-dimensional real normed linear spaces. Next, we give a definition of the Ck space according to [23].
Słowa kluczowe
Wydawca
Rocznik
Tom
21
Numer
1
Strony
25-31
Opis fizyczny
Daty
wydano
2013-01-01
Twórcy
  • Shizuoka City, Japan
  • Shinshu University Nagano, Japan
  • Shinshu University Nagano, Japan
Bibliografia
  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  • [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [4] Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  • [5] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. FormalizedMathematics, 1(3):529-536, 1990.
  • [6] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
  • [7] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [8] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [9] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [10] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
  • [11] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  • [12] Noboru Endou, Hiroyuki Okazaki, and Yasunari Shidama. Higher-order partial differentiation. Formalized Mathematics, 20(2):113-124, 2012. doi:10.2478/v10037-012-0015-z.[Crossref]
  • [13] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1): 35-40, 1990.
  • [14] Takao Inou´e, Adam Naumowicz, Noboru Endou, and Yasunari Shidama. Partial differentiation of vector-valued functions on n-dimensional real normed linear spaces. FormalizedMathematics, 19(1):1-9, 2011. doi:10.2478/v10037-011-0001-x.[Crossref]
  • [15] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990.
  • [16] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992.
  • [17] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.
  • [18] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.
  • [19] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  • [20] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [21] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
  • [22] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • [23] Kosaku Yosida. Functional Analysis. Springer Classics in Mathematics, 1996.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_forma-2013-0002
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