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2011 | 19 | 3 | 139-144
Tytuł artykułu

Continuity of Barycentric Coordinates in Euclidean Topological Spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we present selected properties of barycentric coordinates in the Euclidean topological space. We prove the topological correspondence between a subset of an affine closed space of εn and the set of vectors created from barycentric coordinates of points of this subset.
Słowa kluczowe
Wydawca
Rocznik
Tom
19
Numer
3
Strony
139-144
Opis fizyczny
Daty
wydano
2011-01-01
online
2012-04-26
Twórcy
autor
  • Institute of Informatics, University of Białystok, Poland
Bibliografia
  • Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  • Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.
  • Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990.
  • Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
  • Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • Czesław Byliński. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005.
  • Jing-Chao Chen. The Steinitz theorem and the dimension of a real linear space. Formalized Mathematics, 6(3):411-415, 1997.
  • Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  • Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
  • Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991.
  • Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Convex sets and convex combinations. Formalized Mathematics, 11(1):53-58, 2003.
  • Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Dimension of real unitary space. Formalized Mathematics, 11(1):23-28, 2003.
  • Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
  • Artur Korniłowicz. The correspondence between n-dimensional Euclidean space and the product of n real lines. Formalized Mathematics, 18(1):81-85, 2010, doi: 10.2478/v10037-010-0011-0.[Crossref]
  • Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
  • Anna Lango and Grzegorz Bancerek. Product of families of groups and vector spaces. Formalized Mathematics, 3(2):235-240, 1992.
  • Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.
  • Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • Karol Pąk. Affine independence in vector spaces. Formalized Mathematics, 18(1):87-93, 2010, doi: 10.2478/v10037-010-0012-z.[Crossref]
  • Karol Pąk. Linear transformations of Euclidean topological spaces. Formalized Mathematics, 19(2):103-108, 2011, doi: 10.2478/v10037-011-0016-3.[Crossref]
  • Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
  • Wojciech A. Trybulec. Basis of real linear space. Formalized Mathematics, 1(5):847-850, 1990.
  • Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883-885, 1990.
  • Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.
  • Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-011-0022-5
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