cmi-entrance 2013 QA15

cmi-entrance · India · pgmath 4 marks Not Maths

Let $X$ be a set with the property that for any two metrics $d _ { 1 }$, and $d _ { 2 }$ on $X$, the identity map $$id : \left( X , d _ { 1 } \right) \rightarrow \left( X , d _ { 2 } \right)$$ is continuous. Which of the following are true?
(a) $X$ must be a singleton.
(b) $X$ can be any finite set.
(c) $X$ cannot be infinite.
(d) $X$ may be infinite but not uncountable.

Let $X$ be a set with the property that for any two metrics $d _ { 1 }$, and $d _ { 2 }$ on $X$, the identity map
$$id : \left( X , d _ { 1 } \right) \rightarrow \left( X , d _ { 2 } \right)$$
is continuous. Which of the following are true?\\
(a) $X$ must be a singleton.\\
(b) $X$ can be any finite set.\\
(c) $X$ cannot be infinite.\\
(d) $X$ may be infinite but not uncountable.

Paper Questions

QA1 QA10 QA11 QA12 QA13 QA14 QA15 QA2 QA3 QA4 QA5 QA6 QA7 QA8 QA9 QB1 QB10 QB2 QB3 QB4 QB5 QB6 QB7 QB8 QB9