The Geometric Interior in Real Linear Spaces

Karol Pąk

Formalized Mathematics (2010)

  • Volume: 18, Issue: 3, page 185-188
  • ISSN: 1426-2630

Abstract

top
We introduce the notions of the geometric interior and the centre of mass for subsets of real linear spaces. We prove a number of theorems concerning these notions which are used in the theory of abstract simplicial complexes.

How to cite

top

Karol Pąk. "The Geometric Interior in Real Linear Spaces." Formalized Mathematics 18.3 (2010): 185-188. <http://eudml.org/doc/267146>.

@article{KarolPąk2010,
abstract = {We introduce the notions of the geometric interior and the centre of mass for subsets of real linear spaces. We prove a number of theorems concerning these notions which are used in the theory of abstract simplicial complexes.},
author = {Karol Pąk},
journal = {Formalized Mathematics},
language = {eng},
number = {3},
pages = {185-188},
title = {The Geometric Interior in Real Linear Spaces},
url = {http://eudml.org/doc/267146},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Karol Pąk
TI - The Geometric Interior in Real Linear Spaces
JO - Formalized Mathematics
PY - 2010
VL - 18
IS - 3
SP - 185
EP - 188
AB - We introduce the notions of the geometric interior and the centre of mass for subsets of real linear spaces. We prove a number of theorems concerning these notions which are used in the theory of abstract simplicial complexes.
LA - eng
UR - http://eudml.org/doc/267146
ER -

References

top
  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. 
  2. [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  3. [3] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  4. [4] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  5. [5] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. 
  6. [6] Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Convex sets and convex combinations. Formalized Mathematics, 11(1):53-58, 2003. 
  7. [7] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  8. [8] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. 
  9. [9] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990. 
  10. [10] Karol Pąk. Affine independence in vector spaces. Formalized Mathematics, 18(1):87-93, 2010, doi: 10.2478/v10037-010-0012-z.[Crossref] 
  11. [11] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990. 
  12. [12] Wojciech A. Trybulec. Linear combinations in real linear space. Formalized Mathematics, 1(3):581-588, 1990. 
  13. [13] Wojciech A. Trybulec. Partially ordered sets. Formalized Mathematics, 1(2):313-319, 1990. 
  14. [14] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  15. [15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  16. [16] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 

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.