A⊂B B =⇒A
∅
Rn
Rn0
A⊂Rna∈Rn
A⇐⇒ ∃r > 0, A ⊂B(a, r)
E=RnA E f A Ra= (a1, . . . , an)∈¯
A
f ` a
∀ε > 0,∃η > 0,∀x∈A, hkx−ak6η=⇒ |f(x)−`|6εi
E=RnA E f A Ra= (a1, . . . , an)∈A
f a lim
x→af(x) = f(a)
∀ε > 0,∃η > 0,∀x∈A, hkx−ak6η=⇒ |f(x)−f(a)|6εi
f A f a ∈A
k > 0f:E→Rk
∀x, y ∈E, |f(x)−f(y)|6kkx−yk
f E E
E→R, x 7→ kxk
pi:Rn→R, x = (x1, . . . , xn)7→ xi