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2010 | 18 | 1 | 81-85
Tytuł artykułu

The Correspondence Betweenn-dimensional Euclidean Space and the Product ofnReal Lines

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Wydawca
Rocznik
Tom
18
Numer
1
Strony
81-85
Opis fizyczny
Daty
wydano
2010-01-01
online
2011-01-05
Twórcy
  • Institute of Informatics, University of Białystok, Sosnowa 64, 15-887 Białystok, Poland
Bibliografia
  • [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-010-0011-0
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