The Correspondence Between n -dimensional Euclidean Space and the Product of n Real Lines
Artur Korniłowicz
Formalized Mathematics, Tome 18 (2010), p. 81-85 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:267108 
@article{bwmeta1.element.doi-10_2478_v10037-010-0011-0,
     author = {Artur Korni\l owicz},
     title = {
      The Correspondence Between
      n
      -dimensional Euclidean Space and the Product of
      n
      Real Lines
    },
     journal = {Formalized Mathematics},
     volume = {18},
     year = {2010},
     pages = {81-85},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0011-0}
}

Artur Korniłowicz. 
      The Correspondence Between
      n
      -dimensional Euclidean Space and the Product of
      n
      Real Lines
    . Formalized Mathematics, Tome 18 (2010) pp. 81-85. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0011-0/

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | Zbl 06213858

[2] Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.

[3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

[5] Leszek Borys. Paracompact and metrizable spaces. Formalized Mathematics, 2(4):481-485, 1991.

[6] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.

[7] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.

[8] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

[9] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.

[10] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.

[11] Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991.

[12] Jarosław Gryko. Injective spaces. Formalized Mathematics, 7(1):57-62, 1998.

[13] Stanisława Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Formalized Mathematics, 1(3):607-610, 1990.

[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] Beata Madras. Product of family of universal algebras. Formalized Mathematics, 4(1):103-108, 1993.

[16] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.

[17] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.

[18] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.

[19] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 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.