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Topology Quiz

Authored by Ramana Ginjala

Mathematics

University

Topology Quiz
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40 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following collections is a basis for the standard topology on R?

{(a, b)∣a, b ∈ R, a< b}

{[a, b]∣a, b ∈ R, a < b}

{(a, b)∣a, b ∈ Q, a < b}

{(a, b]∣a, b ∈ R, a < b}

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the standard topology on R, which of the following is NOT an open set?

(0, 1)

[0,1)

n=1∞( 0, 1n )

(−∞,5)

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following subsets of R is dense in the standard topology?

Z (integers)

[0, 1]

Q (rationals)

(0, 1)

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the closure of (0, 1) in the standard topology on R?

(0, 1)

[0, 1)

[0, 1]

(0, 1]

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If B is a basis for a topology τ on X, which of the following is true?

Every element of X belongs to exactly one basis element.

Every open set in τ is a union of basis elements.

The intersection of any two basis elements is always a basis element.

Basis elements are always open sets.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following subsets of R is compact in the standard topology?

(0, 1)

[0, 1)

[0, 1]

(0, ∞)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following subsets of R is connected in the standard topology?

(0,1)∪(2,3)

(0,1)

Q

[0,1]∖{1/2}

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