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• Cell maps
  ...ow the theory of simplicial maps and their homology is extended to general cell complexes. ...esenting the spaces as cell complexes, we examine to what cell in $L$ each cell in $K$ is taken by $f$:
  42 KB (7,005 words) - 03:10, 30 November 2015
• Combinatorial cell maps
  Below, we will see how the theory of simplicial maps is extended to general cell complexes. ...esenting the spaces as cell complexes, we examine to what cell in $L$ each cell in $K$ is taken by $f$:
  31 KB (5,330 words) - 22:14, 14 March 2016
• Homology of maps
  ==Maps of cell complexes== ...ow the theory of simplicial maps and their homology is extended to general cell complexes.
  41 KB (6,926 words) - 02:14, 21 October 2015
• Maps of polyhedra
  ==Maps v. cell maps== ...exes, a map $f:|K|\to |L|$ between their realizations doesn't have to be a cell map. As a result we are unable to define its chain map $f_{\Delta}:C(K)\to
  51 KB (9,162 words) - 15:33, 1 December 2015
• Chain maps
  *(A) $g$ maps each cell in $K$ to a cell in $L$ of the same dimension, otherwise it's $0$. $\\$ This is trouble. Even though we can find a cell for $g(a)$, it can't be $AC$ because it's not in $L$. Therefore, $g(a)$ won
  47 KB (8,115 words) - 16:19, 20 July 2016
• Introduction to discrete calculus, continued
  ==Cell functions== ...to somehow respect the cell structure of ${\mathbb R}$. Let's recall how ''cell functions'' are introduced.
  22 KB (3,661 words) - 13:12, 18 July 2016
• Calculus of chain maps
  ==Cell functions== ...to somehow respect the cell structure of ${\mathbb R}$. Let's recall how ''cell functions'' are introduced.
  41 KB (7,344 words) - 12:52, 25 July 2016
• Topology Illustrated -- Index
  *[[boundary of a cubical cell|boundary of a cubical cell]] *[[cell approximation|cell approximation]]
  16 KB (1,773 words) - 00:41, 17 February 2016
• Simplicial maps and chain maps
  Thus, a simplex is cloned or it is taken to $0$. This behavior is expected. After all, when a simplex is cloned, so is its boundary, face by face:
  34 KB (5,897 words) - 16:05, 26 October 2015
• Euler and Lefschetz numbers
  ...stic''<!--\index{Euler characteristic}--> $\chi (K)$ of an $n$-dimensional cell complex $K$ is the alternating sum of the number of cells in $K$ for each d '''Proposition.''' If $C_k(K)$ is the $k$-chain group of cell complex $K$, then
  41 KB (7,169 words) - 14:00, 1 December 2015
• Simplicial maps
  Thus, a simplex is cloned or it is taken to $0$. This behavior is expected. After all, when a simplex is cloned, so is its boundary, face by face:
  34 KB (5,929 words) - 03:31, 29 November 2015
• Discrete functions
  ...ion of the edge coincides with the direction of the axis. So, for the same cell $[a,b]\subset {\bf R}$, ==Cell functions: nodes and edges==
  15 KB (2,532 words) - 12:21, 11 July 2016
• Algebra on graphs
  ...en to a node, the event that we will call a “collapse”<!--\index{collapsed cell}-->: We say that, in this case, the edge is ''cloned''<!--\index{cloned cell}-->.
  36 KB (6,177 words) - 02:47, 21 February 2016
• Maps of graphs
  <!--150-->[[image:grid with function approximated by cell map.png|center]] We say that, in this case, the edge is ''cloned''<!--\index{cloned}-->.
  29 KB (5,042 words) - 17:57, 28 November 2015