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October 31st, 2011, 06:30 PM   #1
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does open in M imply open in A?

Suppose that A is open in (M,d) and that G is subset of A. Show that G is open in A if and only if G is open in M. Is this still true if we replaced open everywhere by closed?

I have proved the one directon,

suppose G is open in A. Then for all x in A, there existssuch that G. As A is open in (M,d) then for all x in M, there exists such that G A. Therefore G is open in M.

how do i prove the other direction, is this still ture if its closed?
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