Linear Transformations of Euclidean Topological Spaces. Part II

• Autorzy: Karol Pąk
• Języki publikacji: EN

Abstrakty

EN

We prove a number of theorems concerning various notions used in the theory of continuity of barycentric coordinates.

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2011
• Tom: 19
• Numer: 2
• Strony: 109-112

Daty

wydano

2011-01-01

online

2011-07-18

Twórcy

autor

Karol Pąk

• Institute of Informatics, University of Białystok, Poland

Bibliografia

• [1] Jesse Alama. The rank+nullity theorem. Formalized Mathematics, 15(3):137-142, 2007, doi:10.2478/v10037-007-0015-6.[Crossref]
• [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
• [3] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
• [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
• [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
• [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
• [7] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
• [8] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
• [9] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
• [10] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.
• [11] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
• [12] Anna Lango and Grzegorz Bancerek. Product of families of groups and vector spaces. Formalized Mathematics, 3(2):235-240, 1992.
• [13] Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.
• [14] Karol Pąk. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199-211, 2007, doi:10.2478/v10037-007-0024-5.[Crossref]
• [15] Karol Pąk. Affine independence in vector spaces. Formalized Mathematics, 18(1):87-93, 2010, doi: 10.2478/v10037-010-0012-z.[Crossref]
• [16] Karol Pąk. Linear transformations of Euclidean topological spaces. Formalized Mathematics, 19(2):103-108, 2011, doi: 10.2478/v10037-011-0016-3.[Crossref]
• [17] Wojciech A. Trybulec. Basis of real linear space. Formalized Mathematics, 1(5):847-850, 1990.
• [18] Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883-885, 1990.
• [19] Wojciech A. Trybulec. Linear combinations in real linear space. Formalized Mathematics, 1(3):581-588, 1990.
• [20] Wojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1(5):877-882, 1990.
• [21] Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. Formalized Mathematics, 1(2):297-301, 1990.
• [22] Wojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Formalized Mathematics, 1(5):865-870, 1990.
• [23] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
• [24] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
• [25] Xiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541-547, 2005.

Identyfikatory

DOI

10.2478/v10037-011-0017-2