If r>1 not 1/2 then open ball(or sphere ) will be whole metric space X which is not contained in any arbitrary set ..so subset of metric space will not be open ..?Sir please clarify my doubt
I think y should be an element of subset G , not the metric space X because x is an element of G and we are proving that the open ball about x is a subset of G.
Sir jaruri nhi hai ki english me bolkar padhaye aap..aap accha padha rhe hai but sir use hindi language also because sir acche se samjh me bhi aana chahiye n tabhi sir padhne me accha lagta hai
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If r>1 not 1/2 then open ball(or sphere ) will be whole metric space X which is not contained in any arbitrary set ..so subset of metric space will not be open ..?Sir please clarify my doubt
In definition of open set, we say, there exists r > 0, but not for every r > 0
Therefore it is enough to find atleast one r which will satisfy the condition
@@ranjankhatu ohh ..now I understood .sir thanks for clearing my doubt .
I think y should be an element of subset G , not the metric space X because x is an element of G and we are proving that the open ball about x is a subset of G.
@@kumardeepmukhopadhyay7393 no. Simply I am following the definition of Open ball.
Consider (Z, | |) as a subspace of (R, | |), then open balls in Z are
(a) infinite sets
(b) singleton sets
(c) finite sets
(d) None of these
.
Finite sets
Sir please explain
Sir jaruri nhi hai ki english me bolkar padhaye aap..aap accha padha rhe hai but sir use hindi language also because sir acche se samjh me bhi aana chahiye n tabhi sir padhne me accha lagta hai
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