The C k Space

Katuhiko Kanazashi; Hiroyuki Okazaki; Yasunari Shidama

Formalized Mathematics (2013)

  • Volume: 21, Issue: 1, page 25-31
  • ISSN: 1426-2630

Abstract

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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].

How to cite

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Katuhiko Kanazashi, Hiroyuki Okazaki, and Yasunari Shidama. " The C k Space ." Formalized Mathematics 21.1 (2013): 25-31. <http://eudml.org/doc/266706>.

@article{KatuhikoKanazashi2013,
abstract = {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].},
author = {Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {25-31},
title = { The C k Space },
url = {http://eudml.org/doc/266706},
volume = {21},
year = {2013},
}

TY - JOUR
AU - Katuhiko Kanazashi
AU - Hiroyuki Okazaki
AU - Yasunari Shidama
TI - The C k Space
JO - Formalized Mathematics
PY - 2013
VL - 21
IS - 1
SP - 25
EP - 31
AB - 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].
LA - eng
UR - http://eudml.org/doc/266706
ER -

References

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  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. 
  2. [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  3. [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  4. [4] Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990. 
  5. [5] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. FormalizedMathematics, 1(3):529-536, 1990. 
  6. [6] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990. 
  7. [7] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  8. [8] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  9. [9] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  10. [10] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991. 
  11. [11] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. 
  12. [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] Zbl1281.46024
  13. [13] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1): 35-40, 1990. 
  14. [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] Zbl1276.26033
  15. [15] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990. 
  16. [16] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992. 
  17. [17] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990. 
  18. [18] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003. 
  19. [19] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990. 
  20. [20] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  21. [21] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990. 
  22. [22] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  23. [23] Kosaku Yosida. Functional Analysis. Springer Classics in Mathematics, 1996. 

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