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Closed set: Quiz

  

Question 1: However, the compact ________ are "absolutely closed" in a certain sense.
T1 spaceNormal spaceHausdorff spaceTopological space

Question 2: In a ________, a set is closed if and only if it coincides with its closure.
Metric spaceTopological spaceCompact spaceHausdorff space

Question 3: An alternative characterization of closed sets is available via ________ and nets.
SequenceFunction (mathematics)Vector spacePartially ordered set

Question 4: In a first-countable space (such as a metric space), it is enough to consider only convergent ________, instead of all nets.
Partially ordered setMathematicsVector spaceSequence

Question 5: In particular, the ________ and the whole space are closed.
Empty setSet (mathematics)Set theoryTopological space

Question 6: The closed interval [a,b] of ________ is closed.
Transcendental numberReal numberComplex numberIrrational number

Question 7: In a ________, such as in real analysis, a closed set can be defined as a set which contains all its limit points.
Metric spaceCompact spaceTopological spaceTopology

Question 8: The unit interval [0,1] is closed in the metric space real numbers, and the set [0,1] ∩ Q of ________ between 0 and 1 (inclusive) is closed in the space of rational numbers, but [0,1] ∩ Q is not closed in the real numbers.
Irrational numberIntegerComplex numberRational number

Question 9: In topology and related branches of ________, a closed set is a set whose complement is an open set.
Mathematical logicGeometryAlgebraMathematics

Question 10: Sets that can be constructed as the union of ________ closed sets are denoted Fσ sets.
Set (mathematics)Cardinal numberCountable setGeorg Cantor
















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