Have an account?
Skip to Content
Build your own quiz
14 questions
Show Answers
See Preview
- 1. Multiple Choice
Let X be a topological space.
True or false: any subset of X is either open or closed
True
False
- 2. Multiple Choice
The preimage of a path-connected space is path-connected.
True
False
- 3. Multiple Choice
How many cut points of type 2 does the letter Y have?
0
1
2
at least 3
- 4. Multiple Choice
How many cut points of type 2 does ℝ2\{0} have?
0
1
2
at least 3
- 5. Multiple Choice
Which ONE of the following is an OPEN subset of [0,1]?
(-1,1)
[0,0.1)
{ x in ℝ: |x-1|<0.5}
- 6. Multiple Choice
True or false: the image of an open subset under a continuous map is open.
True
False
- 7. Multiple Choice
Let X be given topologies t1 and t2.
True or false: the identity from (X, t1) to (X,t2) is always continuous
True
False
- 8. Multiple Choice
Every closed subset of a compact space is compact.
True
False
- 9. Multiple Choice
Every compact subset of a topological space is closed.
True
False
- 10. Multiple Choice
True or false: The discrete topology is always Hausdorff.
True
False
- 11. Multiple Choice
Let X be a COMPACT topological space, ~ an equivalence relation.
True or false: X/~ with the quotient topology is compact.
True
False
- 12. Multiple Choice
Let I=[0,1]. Consider the space X=I x I, and define an equivalence relation ~ by declaring (0,y)~(1,y) for all y in I.
Which of the following is homeomorphic to X/~?
I x S1
The torus
The sphere S2
The closed disc
- 13. Multiple Choice
True or False: A continuous bijection from a Hausdorff space to a compact space is a homeomorphism.
True
False
- 14. Multiple Choice
True or False: A continuous bijection from X to Y induces an isomorphism on fundamental groups
True
False
- Answer choicesTagsAnswer choicesTags