11). 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 |
|
12). 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 |
|
13). 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 |
|
14). Z is
| A). open in R |
| B). closed in R |
| C). bounded in R |
| D). none of these |
|
15). Every subset of a discrete metric space
| A). only open |
| B). only closed |
| C). both open and closed |
| D). neither open nor closed |
|
16). In with usual metric, every singleton set is
| A). open |
| B). closed |
| C). both open and closed |
| D). none of these |
|
17). In any metric space M, \(\phi\) and M are
| A). open |
| B). closed |
| C). both open and closed |
| D). neither open nor closed |
|
18). Any finite suliset of a metric space is
| A). open |
| B). closed |
| C). both open and closed |
| D). neither open nor closed |
|
19). 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 |
|
20). Let (M, d) be the discrete metric space and A be any subset of A. Then the derived set of A (the set of all limit points of A) is,
| A). A |
| B). M |
| C). \(\phi\) |
| D). \(A^{c}\) |
|
