GATE MA 2018 MA Q34: Topology

Let

be a continuous map from a Hausdorff topological space

to a metric space

. Consider the following two statements:

is a closed map and the inverse image

is compact for each

Q: For every compact subset

, the inverse image

is a compact subset of

Which one of the following is true?

Your answerChoose one option.

Q implies P but P does NOT imply Q

P implies Q but Q does NOT imply P

P and Q are equivalent

neither P implies Q nor Q implies P

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