Let X be a metric space and A⊂X then x∈A^{e} if and only if d(x,A)>0 where A^{e}=the set of points outside
Favorites|Homepage
Subscriptions | sitemap
HOME > > Let X be a metric space and A⊂X then x∈A^{e} if and only if d(x,A)>0 where A^{e}=the set of points outside

Let X be a metric space and A⊂X then x∈A^{e} if and only if d(x,A)>0 where A^{e}=the set of points outside

[From: ] [author: ] [Date: 12-07-05] [Hit: ]
B(x,x ∈ cl(A).......
Let X be a metric space and A⊂X then x∈A^{e} if and only if d(x,A)>0 where A^{e}=the set of points outside

-
We prove the equivalent statement that d(x,A) = 0 if and only if x ∈ cl(A):

d(x,A) = 0 iff

for every r > 0 there exists a ∈ A such that d(x,a) < r iff

for every r > 0, B(x,r) ∩ A ≠ Ø iff

x ∈ cl(A).
1
keywords: the,of,and,be,set,then,outside,if,points,only,isin,where,Let,gt,metric,space,sub,Let X be a metric space and A⊂X then x∈A^{e} if and only if d(x,A)>0 where A^{e}=the set of points outside
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .