Continuity of Barycentric Coordinates in Euclidean Topological Spaces

Karol Pąk

Formalized Mathematics (2011)

  • Volume: 19, Issue: 3, page 139-144
  • ISSN: 1426-2630

Abstract

top
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.

How to cite

top

Karol Pąk. "Continuity of Barycentric Coordinates in Euclidean Topological Spaces." Formalized Mathematics 19.3 (2011): 139-144. <http://eudml.org/doc/267650>.

@article{KarolPąk2011,
abstract = {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.},
author = {Karol Pąk},
journal = {Formalized Mathematics},
language = {eng},
number = {3},
pages = {139-144},
title = {Continuity of Barycentric Coordinates in Euclidean Topological Spaces},
url = {http://eudml.org/doc/267650},
volume = {19},
year = {2011},
}

TY - JOUR
AU - Karol Pąk
TI - Continuity of Barycentric Coordinates in Euclidean Topological Spaces
JO - Formalized Mathematics
PY - 2011
VL - 19
IS - 3
SP - 139
EP - 144
AB - 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.
LA - eng
UR - http://eudml.org/doc/267650
ER -

References

top
  1. Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. 
  2. Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  3. Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990. 
  4. Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  5. Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990. 
  6. Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 
  7. Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  8. Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  9. Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  10. Czesław Byliński. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005. 
  11. Jing-Chao Chen. The Steinitz theorem and the dimension of a real linear space. Formalized Mathematics, 6(3):411-415, 1997. 
  12. Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. 
  13. Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991. 
  14. Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991. 
  15. Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Convex sets and convex combinations. Formalized Mathematics, 11(1):53-58, 2003. 
  16. Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Dimension of real unitary space. Formalized Mathematics, 11(1):23-28, 2003. 
  17. Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  18. 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] 
  19. Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990. 
  20. Anna Lango and Grzegorz Bancerek. Product of families of groups and vector spaces. Formalized Mathematics, 3(2):235-240, 1992. 
  21. Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996. 
  22. Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990. 
  23. Karol Pąk. Affine independence in vector spaces. Formalized Mathematics, 18(1):87-93, 2010, doi: 10.2478/v10037-010-0012-z.[Crossref] 
  24. Karol Pąk. Linear transformations of Euclidean topological spaces. Formalized Mathematics, 19(2):103-108, 2011, doi: 10.2478/v10037-011-0016-3.[Crossref] Zbl1276.15002
  25. Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990. 
  26. Wojciech A. Trybulec. Basis of real linear space. Formalized Mathematics, 1(5):847-850, 1990. 
  27. Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883-885, 1990. 
  28. Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  29. Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  30. Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  31. Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  32. Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992. 
  33. Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.