List of symbols

Numbers
${\mathbb{N}}$		natural numbers
${\mathbb{Z}}$		integer numbers
${\mathbb{Z}^+}$		integer positive numbers
Elements of cellular automata
${K^{}}$		set of states
${k^{}}$		number of states
${{c}_{}}$		configuration
${r_{}}$		neighborhood radius
${\varphi}$		local rule evolution
${\varphi^{-1}}$		inverse local rule of ${\varphi}$
${{K^{2{r_{}}+1}}}$		family of neighborhoods
${{C}_{}}$		set of configurations
${\Phi}$		mapping between configurations induced by ${\varphi}$
${\Phi^{-1}}$		inverse mapping of ${\Phi}$
Sequences of elements of ${K^{}}$
${w_{}}$		state sequence
${{K^{}}^*}$		set of finite state sequences
${[a_i,a_f]}$		sequence beginning in position $a_i$ and ending in position $a_f$

Centered cylinder Set
${\mathcal{C}_{[{w_{}}]}}$		cylinder set centered in sequence ${w_{}}$
${\mathfrak{C}_{}}$		family of centered cylinder sets
Generic sets and generic spaces
${{X}_{}}$		generic set
${x_{}}$		generic element
${\underset{}{\cap}}$		intersection of sets
${\mathcal{O}_{}}$		open set
${\mathit{d}}$		generic distance
${{\mathit{d}}({x_{1}},{x_{2}})}$		distance between elements ${x_{1}}$ and ${x_{2}}$
$\Psi$		generic global mapping
$({{X}_{}},\Psi)$		generic dynamical system
Configuration space
${({{C}_{}},{\mathfrak{C}_{}})}$		topological configuration space
${{\varphi} \circ {\varphi}}$		composition of evolution rules
${\mathit{e}_{}}$		configuration sequence
$({{C}_{}},{\Phi})$		dynamical system of cellular automata