Thread: metric Space , series , open ball

Hello ,
can someone tell me if this conditions are equivalent

(i) there exists epsilon> 0 such that the open ball of radius epsilon around x is a singleton:
Be (x) = (x)

(ii) if a sequence (xn) of points of X approaches x, then (xn) is eventually
constant.

Any help is welcome

thank you in advance

please help

i have the same question

any help?

thanks

solved