Peano曲线的推扩

Extention of Peano Curve

定理1 存在连续映射:f,f:E1→E2满足,f(E1)=E2.定理2 ACE1f是连续单调映射f:A→E1满足:supx∈A{f(x)}=Mimfx∈A{f(x)}=N则f连续扩充到E1上.

Theory1:exist continuous mapping f f:E^1→E^2 f(E^1)=E^2 Theory2:f:A→E^1 ACE^1,f continuous monotone mapping,satisfy (sup)x∈A{f(x)}=M(inf)x∈A{f(x)}=N Then f continuous momotone extention on E^1.