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Homeomorphism: Quiz

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Question 1: Isometric isomorphism is an isomorphism between ________
TopologyTopological spaceCompact spaceMetric space

Question 2: Thus, a square and a ________ are homeomorphic to each other, but a sphere and a doughnut are not.
CircleConic sectionPiPolar coordinate system

Question 3: A function f: XY between two ________ (X, TX) and (Y, TY) is called a homeomorphism if it has the following properties:
Compact spaceTopological spaceHausdorff spaceMetric space

Question 4: The product space S1 × S1 and the two-dimensional ________ are homeomorphic.
TorusManifoldMöbius stripStereographic projection

Question 5: Any ________ with a single point removed is homeomorphic to the set of all points in R2 (a 2-dimensional plane).
ManifoldGeometry3-sphereSphere

Question 6: For example, if one of them is compact, then the other is as well; if one of them is connected, then the other is as well; if one of them is Hausdorff, then the other is as well; their homotopy & ________ will coincide.
Homology (mathematics)Algebraic topologyHomological algebraGroup cohomology

Question 7: For some purposes, the homeomorphism group happens to be too big, but by means of the ________ relation, one can reduce this group to the mapping class group.
HomotopyHomotopy groupFundamental groupTopology

Question 8: The open interval (−1, +1) is homeomorphic to the ________ R.
Irrational numberReal numberTranscendental numberComplex number

Question 9: The homeomorphisms form an ________ on the class of all topological spaces.
Group (mathematics)Group actionEquivalence relationBinary relation

Question 10: Two homeomorphic spaces share the same ________.
TopologyNormal spaceTopological propertyTrivial topology







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