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Any subspace of a complete metric space is

 A) complete B) closed C) need not be complete D) none of these

 C) need not be complete

A = (1, 2] is a subspace of a complete metric space R.

But A = (1, 2] is not complete.

Part of solved Real Analysis questions and answers : >> Elementary Mathematics >> Real Analysis

Similar Questions
1). Any subset A of a complete metric space is complete if and only if
 A). A is closed B). A is open C). A is finite D). A is countable
2). A complete metric space is of
 A). first category B). second category C). both (A) and (B) D). none of these
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 A). second category B). first category C). third category D). none of these
4). Any discrete metricspace is
 A). first category B). second category C). third category D). none of these
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6). M is an infinite set with discrete metric Then
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7). Let M be a subspace of R where $$M= [1,2]\cup [3,4]$$ then $$[1,2]$$ is
 A). $$\left( 0,\frac{1}{2} \right]$$ is not Open in [0, 2] B). $$\left( 0,\frac{1}{2} \right]$$ is open in [0, 2] C). $$\left( 0,\frac{1}{2} \right]$$ is closed in [0, 2] D). None of these