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Topology: Quiz

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Question 1: If the function maps the real numbers to the real numbers (both spaces with the Standard Topology), then this definition of continuous is equivalent to the definition of continuous in ________.
Differential calculusIntegralDerivativeCalculus

Question 2: More is true: In Rn, a set is compact ________ it is closed and bounded.
First-order logicLogical connectivePropositional calculusIf and only if

Question 3: Every path-connected, locally path-connected and semi-locally simply connected space has a ________.
Covering spaceGroup actionCovering groupFundamental group

Question 4: Every continuous bijection from a ________ to a Hausdorff space is necessarily a homeomorphism.
Metric spaceTopological spaceHilbert spaceCompact space

Question 5: Every ________ of points in a compact metric space has a convergent subsequence.
SequenceVector spaceMathematicsPartially ordered set

Question 6: Cantor, in addition to setting down the basic ideas of set theory, considered point sets in ________, as part of his study of Fourier series.
Euclidean spaceDimensionMathematicsVector space

Question 7: Every compact m-________ can be embedded in some Euclidean space Rn.
Differentiable manifoldDifferential geometryManifoldGeometry

Question 8: ________ groups (including the fundamental group).
HomeomorphismTopologyHomotopy groupHomotopy

Question 9: In 1914, Felix Hausdorff coined the term "topological space" and gave the definition for what is now called a ________.
Hausdorff spaceTychonoff spaceNormal spaceT1 space

Question 10: For further developments, see point-set topology and ________.
Algebraic topologyCategory theoryAbstract algebraMathematics







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