GATE MA topic:topology PYQs & Answers

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topic:topology

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Questions 1–10 of 46. Imported answers require independent review unless marked reviewed.

Topic practice 46 questionsPage 1 of 5

Consider

with the topology

Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

is a Hausdorff space.

Any finite subset of

is closed.

is compact.

is connected.

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The number of distinct topologies on the set

consisting of exactly four elements is equal to ________. (answer in integer)

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Let

and

be topological spaces and

be a continuous and bijective mapping. Which one of the following statements is TRUE?

Your answerChoose one option.

is a homeomorphism if

and

are compact.

is a homeomorphism if

is Hausdorff and

is compact.

is a homeomorphism if

is compact and

is Hausdorff.

is a homeomorphism if

and

are Hausdorff.

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Let

with usual topology. Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

is not compact.

is compact.

is connected.

is not connected.

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Let

be equipped with the topology

. Then the number of subsets of

which are neither open nor closed is ________. (answer in integer)

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Let

be diagonalizable and

, where

. Then, which one of the following is TRUE?

Your answerChoose one option.

is compact and connected

is neither compact nor connected

is compact but not connected

is connected but not compact

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Consider the following subsets of the Euclidean space

, and

Then, which one of the following is TRUE?

Your answerChoose one option.

is connected, but

and

are not connected

and

are connected, but

is not connected

and

are connected, but

is not connected

and

are connected, but

is not connected

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In the following, all subsets of Euclidean spaces are considered with the respective subspace topologies. Define an equivalence relation

on the sphere

, for

. Let

denote the equivalence class of

, and let

denote the set of all such equivalence classes. Let

be given by

. If

is provided with the quotient topology induced by the map

, then which one of the following is TRUE?

Your answerChoose one option.

is homeomorphic to

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Consider the metric spaces

and

with the metrics defined by

and

, respectively. Then, which one of the following is TRUE?

Your answerChoose one option.

is open in

but not in

is open in

but not in

is open in both

and

is open neither in

nor in

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Let

and

be provided with the respective Euclidean topologies, and let

be assigned the subspace topology induced from

. If

is a non-constant continuous function, then which of the following is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

maps closed sets to closed sets

is injective

is surjective

There exists

such that

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GATE MA topic:topology PYQs

How to practice topic:topology

Question 24

Question 34

Question 47

Question 49

Question 62

Question 11

Question 15

Question 44

Question 46

Question 57