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 |
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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 |
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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 |
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14). Z is
A). open in R |
B). closed in R |
C). bounded in R |
D). none of these |
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15). Every subset of a discrete metric space
A). only open |
B). only closed |
C). both open and closed |
D). neither open nor closed |
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16). In with usual metric, every singleton set is
A). open |
B). closed |
C). both open and closed |
D). none of these |
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17). In any metric space M, \(\phi\) and M are
A). open |
B). closed |
C). both open and closed |
D). neither open nor closed |
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18). Any finite suliset of a metric space is
A). open |
B). closed |
C). both open and closed |
D). neither open nor closed |
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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 |
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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). \(A^{c}\) |
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