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Topological space: Quiz


Question 1: A function between topological spaces is said to be continuous if the ________ of every open set is open.
Image (mathematics)Set (mathematics)Set theoryBinary relation

Question 2:
Which of the following titles did Topological space have?
Topological Methods in the Theory of Nonlinear Integral Equations
Topological space
Noetherian topological space
Topological field

Question 3: A topological space is a set X together with τ, a collection of subsets of X, satisfying the following ________:
AxiomMathematical logicSet theoryAxiomatic system

Question 4: Such spaces are called ________.
Sierpiński spaceFinite topological spaceTopological indistinguishabilitySpecialization (pre)order

Question 5: The collection of all topologies on a given fixed set X forms a ________: if F = {τα : α in A} is a collection of topologies on X, then the meet of F is the intersection of F, and the join of F is the meet of the collection of all topologies on X which contain every member of F.
SemilatticeComplete latticeOrder theoryLattice (order)

Question 6: They appear in virtually every branch of modern ________ and are a central unifying notion.
Mathematical logicMathematicsGeometrySet theory

Question 7: This leads to concepts such as topological groups, topological vector spaces, topological rings and ________.
Group (mathematics)Field (mathematics)Local fieldPrime number

Question 8: The ________ is defined algebraically on the spectrum of a ring or an algebraic variety.
Algebraic geometryZariski topologyPolynomial ringField (mathematics)

Question 9: ________ embody a metric, a precise notion of distance between points.
TopologyCompact spaceMetric spaceTopological space

Question 10: Topological spaces can be broadly classified, up to homeomorphism, by their ________.
Normal spaceTrivial topologyTopologyTopological property


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