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Introduction to Topology

Topological Logic Quiz

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Which of the following is a topological space?

  1. A set of points with a distance function
  2. A set of points with an open set operation
  3. A set of points with a closed set operation
  4. A set of points with a topology
Question 2 Multiple Choice (Single Answer)

What is the closure of a set in a topological space?

  1. The smallest closed set containing the set
  2. The largest open set containing the set
  3. The set of all points that are limit points of the set
  4. The set of all points that are interior points of the set
Question 3 Multiple Choice (Single Answer)

What is the interior of a set in a topological space?

  1. The largest open set contained in the set
  2. The smallest closed set containing the set
  3. The set of all points that are limit points of the set
  4. The set of all points that are interior points of the set
Question 4 Multiple Choice (Single Answer)

What is a continuous function between two topological spaces?

  1. A function that preserves open sets
  2. A function that preserves closed sets
  3. A function that preserves both open and closed sets
  4. A function that preserves neither open nor closed sets
Question 5 Multiple Choice (Single Answer)

What is a homeomorphism between two topological spaces?

  1. A continuous function that is also a bijection
  2. A continuous function that is also a surjection
  3. A continuous function that is also an injection
  4. A continuous function that is also a bijection and a surjection
Question 6 Multiple Choice (Single Answer)

What is the product topology on the product of two topological spaces?

  1. The topology generated by the open sets of the two spaces
  2. The topology generated by the closed sets of the two spaces
  3. The topology generated by both the open and closed sets of the two spaces
  4. The topology generated by neither the open nor closed sets of the two spaces
Question 7 Multiple Choice (Single Answer)

What is the quotient topology on the quotient space of a topological space?

  1. The topology generated by the open sets of the quotient space
  2. The topology generated by the closed sets of the quotient space
  3. The topology generated by both the open and closed sets of the quotient space
  4. The topology generated by neither the open nor closed sets of the quotient space
Question 8 Multiple Choice (Single Answer)

What is the subspace topology on a subspace of a topological space?

  1. The topology generated by the open sets of the subspace
  2. The topology generated by the closed sets of the subspace
  3. The topology generated by both the open and closed sets of the subspace
  4. The topology generated by neither the open nor closed sets of the subspace
Question 9 Multiple Choice (Single Answer)

What is the Sorgenfrey line?

  1. A topological space that is homeomorphic to the real line
  2. A topological space that is homeomorphic to the unit interval
  3. A topological space that is homeomorphic to the Cantor set
  4. A topological space that is homeomorphic to the Sierpinski carpet
Question 10 Multiple Choice (Single Answer)

What is the Cantor set?

  1. A topological space that is homeomorphic to the real line
  2. A topological space that is homeomorphic to the unit interval
  3. A topological space that is homeomorphic to the Sorgenfrey line
  4. A topological space that is homeomorphic to the Sierpinski carpet
Question 11 Multiple Choice (Single Answer)

What is the Sierpinski carpet?

  1. A topological space that is homeomorphic to the real line
  2. A topological space that is homeomorphic to the unit interval
  3. A topological space that is homeomorphic to the Cantor set
  4. A topological space that is homeomorphic to the Sorgenfrey line
Question 12 Multiple Choice (Single Answer)

What is the Alexander horned sphere?

  1. A topological space that is homeomorphic to the real line
  2. A topological space that is homeomorphic to the unit interval
  3. A topological space that is homeomorphic to the Cantor set
  4. A topological space that is homeomorphic to the Sierpinski carpet
Question 13 Multiple Choice (Single Answer)

What is the Menger sponge?

  1. A topological space that is homeomorphic to the real line
  2. A topological space that is homeomorphic to the unit interval
  3. A topological space that is homeomorphic to the Cantor set
  4. A topological space that is homeomorphic to the Sierpinski carpet
Question 14 Multiple Choice (Single Answer)

What is the Knaster-Kuratowski fan?

  1. A topological space that is homeomorphic to the real line
  2. A topological space that is homeomorphic to the unit interval
  3. A topological space that is homeomorphic to the Cantor set
  4. A topological space that is homeomorphic to the Sierpinski carpet
Question 15 Multiple Choice (Single Answer)

What is the Warsaw circle?

  1. A topological space that is homeomorphic to the real line
  2. A topological space that is homeomorphic to the unit interval
  3. A topological space that is homeomorphic to the Cantor set
  4. A topological space that is homeomorphic to the Sierpinski carpet
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