Re:Re:metric 관련 문제 입니다.

[비는아픔]

쓰고나니 notation이 너무 조잡스럽네요...;

: a metric on defined by

: the standard metric on

Suppose is an extended metric of on

and the induced topology by the metric is equal to the standard topology of .

Let be the product topology of

and be the product topology of .

Observe that is continuous.(well-known)

Consider a sequence on with .

Then since converges to over .

However, trivially goes to  ( so there exists no such .

[비는아픔]

에고 그냥 수열 (1/n) 생각하면 끝나는거였군요; usual에서는 0으로 수렴하나 D에서는 Cauchy가 아니니... 에휴 삽질 ㅋㅋ