GATE MA Topology PYQs & Answers — Page 5

Questions 41–46 of 46. Imported answers require independent review unless marked reviewed.

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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Let

denote

endowed with the usual topology. Let

denote

endowed with the co-finite topology. If

is the product topological space

, then

Your answerChoose one option.

the topology of

is the same as the topology of $Z

the topology of

is strictly coarser (weaker) than that of

the topology of

is strictly coarser (weaker) than that of

the topology of

cannot be compared with that of

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Consider

with the usual topology for

. Each of the following options gives topological spaces

and

with respective induced topologies. In which option is

homeomorphic to

Your answerChoose one option.

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Let

and

be topological spaces and let

be a continuous surjective function. Which one of the following statements is TRUE?

Your answerChoose one option.

is separable, then

is separable

is first countable, then

is first countable

is Hausdorff, then

is Hausdorff

is regular, then

is regular

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Consider the topology

. Then, the topological space

Your answerChoose one option.

compact but NOT connected

connected but NOT compact

both compact and connected

neither compact nor connected

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Let

and

denote the usual topology and the discrete topology on

, respectively. Consider the following three topologies:

Then

Your answerChoose one option.

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GATE MA Topology PYQs

Question 34

Question 35

Question 36

Question 19

Question 20

Question 45