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The fundamental polygon of is a -gon which gives a CW-structure with one 2-cell, 1-cells, and one 0-cell. The 2-cell is attached along the boundary of the -gon, which contains every 1-cell twice, once forwards and once backwards. This means the attaching map is zero, since the forwards and backwards directions of each 1-cell cancel out.
It admits a CW structure with one cell in each dimension. The terminology for a generic 2-dimensional CW complex is a shadow. [8] A polyhedron is naturally a CW complex. Grassmannian manifolds admit a CW structure called Schubert cells. Differentiable manifolds, algebraic and projective varieties have the homotopy type of CW complexes.
If is cellular with cell-datum (,,,) and is an ideal (a downward closed subset) of the poset then ():= (where the sum runs over and , ()) is a two-sided, -invariant ideal of and the quotient / is cellular with cell datum (,,,) (where i denotes the induced involution and M, C denote the restricted mappings).
A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell.
In mathematics and computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors.
Light micrograph of a moss's leaf cells at 400X magnification. The following outline is provided as an overview of and topical guide to cell biology: . Cell biology – A branch of biology that includes study of cells regarding their physiological properties, structure, and function; the organelles they contain; interactions with their environment; and their life cycle, division, and death.
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