The C k Space
Katuhiko Kanazashi ; Hiroyuki Okazaki ; Yasunari Shidama
Formalized Mathematics, Tome 21 (2013), p. 25-31 / Harvested from The Polish Digital Mathematics Library
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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].

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:266706 
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      The C
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     pages = {25-31},
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Katuhiko Kanazashi; Hiroyuki Okazaki; Yasunari Shidama. 
      The C
      k
      Space
    . Formalized Mathematics, Tome 21 (2013) pp. 25-31. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0002/

[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] | Zbl 1281.46024

[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] | Zbl 1276.26033

[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.