Topology MCQs Quiz.2 || Compactness, Complete Space

There are Topology Compactness MCQs with correct answers for entry test preparations. After solving these MCQs you will get better results in your university entry test exam or interviews. So please solve these MCQs carefully. If you are interested to solve more Quiz then must visit Real numbers system MCQs, Random variables MCQs, and other important quizzes for preparations, Quiz.1, Quiz.2, Quiz.3, Quiz.4, Quiz.5.

Topology MCQs Quiz.2:

Topology MCQs With Correct Answers

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1. Every compact subset of a T₂ - space is

a) Open

b) Closed

c) Bounded

d) Unboubed

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2. Open interval (5,7) is

a) Compact

b) Not compact

c) Countable

d) Separable

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3. Which of the following is true?

a) A is compact with respect to topology on A implies A is compact with respect to relative topology on A

b) A is compact with respect to relative topology on A implies A is compact with respect to topology on A

c) A is compact with respect to topology on A if and only if A is compact with respect to relative topology on A

d) None of these

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4. Arc wise connected set A is

a) Connected

b) Not connnected

c) Separated

d) Not separated

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5. A compact subset of a metric space is

a) Countable

b) Sequentially compact

c) Both a and b

d) None of these

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6. If A is compact and B is closed, then ...... is compact

a) A U B

b) A ∩ B

c) A-B

d) None of these

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7. An infinite subset of a discrete topological space is

a) Compact

b) Not compact

c) Sequentially compact

d) Countably compact

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8. Continuous images of connected sets are ......

a) Connected

b) Not connected

c) Compact

d) None of these

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9. Region is ........... set

a) Open

b) Connected

c) Open and connected

d) Open but not connected

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10. Sequentially compact sets are

a) Totally bounded

b) Bounded

c) Both a and b

d) Unbounded

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11. The ........ of connected spaces is connected

a) Union

b) Intersection

c) Product

d) Sum

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12. A subset of a compact space

a) Is compact

b) Need not to be compact

c) Is countable

d) Is separable

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13. If A and B are non-empty separated sets, then A U B is

a) Connected

b) Disconnected

c) Separated

d) Separable

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14. A topological space X is ........ compact if and only if every point in X has a compact neighborhood

a) Locally

b) Sequentially

c) Countable

d) All of these

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15. If X is connected , then component(s) of X is(are)

a) Empty set

b) X

c) Empty set and X

d) None of these

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