The Correspondence Between n -dimensional Euclidean Space and the Product of n Real Lines

Artur Korniłowicz

Formalized Mathematics (2010)

  • Volume: 18, Issue: 1, page 81-85
  • ISSN: 1426-2630

Abstract

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In the article we prove that a family of open n-hypercubes is a basis of n-dimensional Euclidean space. The equality of the space and the product of n real lines has been proven.

How to cite

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Artur Korniłowicz. " The Correspondence Between n -dimensional Euclidean Space and the Product of n Real Lines ." Formalized Mathematics 18.1 (2010): 81-85. <http://eudml.org/doc/267108>.

@article{ArturKorniłowicz2010,
abstract = {In the article we prove that a family of open n-hypercubes is a basis of n-dimensional Euclidean space. The equality of the space and the product of n real lines has been proven.},
author = {Artur Korniłowicz},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {81-85},
title = { The Correspondence Between n -dimensional Euclidean Space and the Product of n Real Lines },
url = {http://eudml.org/doc/267108},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Artur Korniłowicz
TI - The Correspondence Between n -dimensional Euclidean Space and the Product of n Real Lines
JO - Formalized Mathematics
PY - 2010
VL - 18
IS - 1
SP - 81
EP - 85
AB - In the article we prove that a family of open n-hypercubes is a basis of n-dimensional Euclidean space. The equality of the space and the product of n real lines has been proven.
LA - eng
UR - http://eudml.org/doc/267108
ER -

References

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  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  2. [2] Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990. 
  3. [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  4. [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  5. [5] Leszek Borys. Paracompact and metrizable spaces. Formalized Mathematics, 2(4):481-485, 1991. 
  6. [6] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990. 
  7. [7] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 
  8. [8] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  9. [9] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990. 
  10. [10] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991. 
  11. [11] Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991. 
  12. [12] Jarosław Gryko. Injective spaces. Formalized Mathematics, 7(1):57-62, 1998. 
  13. [13] Stanisława Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Formalized Mathematics, 1(3):607-610, 1990. 
  14. [14] Artur Korniłowicz. Arithmetic operations on functions from sets into functional sets. Formalized Mathematics, 17(1):43-60, 2009, doi:10.2478/v10037-009-0005-y.[Crossref] 
  15. [15] Beata Madras. Product of family of universal algebras. Formalized Mathematics, 4(1):103-108, 1993. 
  16. [16] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990. 
  17. [17] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990. 
  18. [18] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990. 
  19. [19] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 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. 

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