i'm studying on pma of walter rudin
i got a question about theorem 2.27 ; if x is a metric space and еcx then \bar e is closed. (\bar e means closure of e)
proof as follows; if pex and p e then p is neither a point of e nor a limit point of e. hence p has a neighborhood which does not intersect e.
"the complement of \bar{e} is therfore open." ; i can't understand this; i understand that the complement of e is open because there exists a neighborhood n of p s. t n \subset e^c
then how can i sure n c e ? ? !