Topological Vector Space

1. 기초 함수들

vector addition:conti(open, closed, V, bdd 보존)

scalar multiplication:conti

translation:homeomorphism(open, closed, V, bdd 보존)

multiplication:homeomorphism(open, closed, V, bdd 보존)

2. Topology

E+open=open

s*open=open

s*nbd of x=nbd of x

the topological structure of tvs is determined by any local open neighbourhood base at 0.

for any nbd of 0, there exists nbd2 of 0 s.t. nbd2+nbd2 is a subset of nbd1 and nbd2=(-nbd2)

tvs가 T2<->tvs가 T1

nbd of 0=A

3. Theorem

open S is 전체 tvs 뿐이다.

f-d