Jump to ContentJump to Main Navigation
Show Summary Details

Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2015: 0.134
Source Normalized Impact per Paper (SNIP) 2015: 0.686
Impact per Publication (IPP) 2015: 0.296

Open Access
Online
ISSN
1898-9934
See all formats and pricing
Volume 18, Issue 1 (Jan 2010)

Issues

Abstract Simplicial Complexes

Karol Pąk
  • Institute of Informatics, University of Białystok, Poland
Published Online: 2011-01-05 | DOI: https://doi.org/10.2478/v10037-010-0013-y

Abstract Simplicial Complexes

In this article we define the notion of abstract simplicial complexes and operations on them. We introduce the following basic notions: simplex, face, vertex, degree, skeleton, subdivision and substructure, and prove some of their properties.

  • [1] Broderick Arneson and Piotr Rudnicki. Recognizing chordal graphs: Lex BFS and MCS. Formalized Mathematics, 14(4):187-205, 2006, doi:10.2478/v10037-006-0022-z. [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. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

  • [5] Grzegorz Bancerek. Tarski's classes and ranks. Formalized Mathematics, 1(3):563-567, 1990.

  • [6] Grzegorz Bancerek. Continuous, stable, and linear maps of coherence spaces. Formalized Mathematics, 5(3):381-393, 1996.

  • [7] Grzegorz Bancerek and Yasunari Shidama. Introduction to matroids. Formalized Mathematics, 16(4):325-332, 2008, doi:10.2478/v10037-008-0040-0. [Crossref]

  • [8] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

  • [9] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

  • [10] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

  • [11] Adam Naumowicz. On Segre's product of partial line spaces. Formalized Mathematics, 9(2):383-390, 2001.

  • [12] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.

  • [13] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.

  • [14] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.

  • [15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

  • [16] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

About the article


Published Online: 2011-01-05

Published in Print: 2010-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-010-0013-y. Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Karol Pąk
Formalized Mathematics, 2011, Volume 19, Number 3
[2]
Karol Pąk
Formalized Mathematics, 2010, Volume 18, Number 4

Comments (0)

Please log in or register to comment.
Log in