Spaces with a finite family of basic functions
Spaces with a finite family of basic functions
Let X be a T1 completely regular space. A family Φ⊆ C(X) is basic for X if each f∈C(X) can be written as: f = ∑ q = 1 n ( g ρ ∘ Φ q ) , for some Φ1, …, Φn∈Φ and g1, …, gn∈C(ℝ). Then X has …