Continuous Functions. Jacques Simon

n]] integer interval: [[m, n]] = {i ∈ ℕ* : m ≤ i ≤ n} [[m, ∞]] extended integer interval: [[m, ∞]] = {i ∈ ℕ* : i ≥ m} ⋃ {∞} (a,b) open interval: (a, b) = {x ∈ ℝ : a < x < b} [a,b] closed interval: [a, b] = {x ∈ ℝ : a ≤ x ≤ b} ⋐ compact inclusion in ℝ^d ⊂ algebraic inclusion \ set difference: U \ V = {u ∈ U : u∉ V} × product: U × V = {(u, υ) : u ∈ U, υ ∈ V} ø empty set

      SPECIAL FUNCTIONS

det	determinant
e	exponential number
log	logarithm
	concentrated flow
α	localizing function, partition of unity
ρn	regularizing function
ψ	divergence-free test field
Ψ	tubular flow
ϒ	function whose graph defines a surface

      TYPOGRAPHY

▌	end of statement
	end of proof or remark