Any discrete metricspace is


A) first category

B) second category

C) third category

D) none of these

Correct Answer:
B) second category

Description for Correct answer:
Any complete metric space is of second category.

Discrete metric space is complete.

Therefore any complete metric space is of second category.

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








Comments

No comments available




Similar Questions
1). Any discrete metric space having more than one point is
A). connected
B). finite
C). null set
D). disconnected
-- View Answer
2). 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
3). 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
4). 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
5). Z is
A). open in R
B). closed in R
C). bounded in R
D). none of these
-- View Answer


6). 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
7). In with usual metric, every singleton set is
A). open
B). closed
C). both open and closed
D). none of these
-- View Answer
8). In any metric space M, \(\phi\) and M are
A). open
B). closed
C). both open and closed
D). neither open nor closed
-- View Answer
9). Any finite suliset of a metric space is
A). open
B). closed
C). both open and closed
D). neither open nor closed
-- View Answer
10). A subset M of \(R^{2}\) is compact if and only if M is ____.
A). closed
B). bounded
C). closed and bounded
D). none of these
-- View Answer