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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
3). R is of
 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
5). Any discrete metric space having more than one point is
 A). connected B). finite C). null set D). disconnected

6). M is an infinite set with discrete metric Then
 A). M is compact B). M is connected C). M is not compact D). None of these
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