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

Correct Answer:
A) A is closed

Description for Correct answer:
Any subset A of a complete metric space M is complete if and only if A is closed.

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








Comments

No comments available




Similar Questions
1). A complete metric space is of
A). first category
B). second category
C). both (A) and (B)
D). none of these
-- View Answer
2). R is of
A). second category
B). first category
C). third category
D). none of these
-- View Answer
3). Any discrete metricspace is
A). first category
B). second category
C). third category
D). none of these
-- View Answer
4). Any discrete metric space having more than one point is
A). connected
B). finite
C). null set
D). disconnected
-- View Answer
5). 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
-- View Answer


6). Let M be a subspace of R where \(M= [1,2]\cup [3,4]\) then \([1,2]\) is
A). open in M
B). closed in M
C). both open and closed in M
D). neither open nor closed in M
-- View Answer
7). It R be the metric space then,
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
-- View Answer
8). Z is
A). open in R
B). closed in R
C). bounded in R
D). none of these
-- View Answer
9). Every subset of a discrete metric space
A). only open
B). only closed
C). both open and closed
D). neither open nor closed
-- View Answer
10). In with usual metric, every singleton set is
A). open
B). closed
C). both open and closed
D). none of these
-- View Answer