Fall11.practice - MGF3301 — practice questions December 8 2011 The final exam will consist of two parts the first part will refer to material

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Unformatted text preview: MGF3301 — practice questions December 8, 2011 The final exam will consist of two parts: the first part will refer to material covered in the two midterms; the second (longer) part will be based on the material we covered since the second midterm: completeness of Dedekind cuts, cardinality, and topology. (The first part will be worth 10 points; the second, 20 points.) The following questions deal with the material covered in the second part. They are not meant to look like exam questions, rather like study points. If you cannot confidently answer all these questions without looking up the class notes, then you are certainly not ready for the final exam! • What is the ‘least upper bound property’? Does Q satisfy it? Does D? Why? • What is the ‘cardinality’ of a set? Can you give examples of sets with different cardinalities? • What does ‘uncountable’ mean? • Why is there no ‘set of all sets’? • What does the Cantor-Bernstein-Schr¨ der theorem say? o • What is a topology? What is a topological space? What is the ‘induced’ topology on a subset of a topological space? • How do you define the open sets in the standard topology on R? on Rn ? • Can you give examples of sets that are closed, open, or neither in R with the standard topology? with the Zariski topology? • What is the topological definition of ‘continuous function’? • What is a ‘homeomorphism’? Can you give examples of spaces that are/are not homeomorphic? 1 ...
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This note was uploaded on 12/14/2011 for the course MGF 3301 taught by Professor Aluffi during the Fall '11 term at FSU.

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