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1. Show that the set R\Q of irrational numbers, with usual topology (relative topology from R), is topologically complete.
2. Define a complete metric for R\{0, 1} with usual (relative) topology.
3. Define a complete metric for the usual (relative) topology on R\Q.
4. (a) If (S, d) is a complete metric space, X is a Gδ subset of S, and for the relative topology on X, Y is a Gδ subset of X , show that Y is a Gδ in S.
(b) Prove the same for a general topological space S.
5. Show that the plane R2 is not a countable union of lines (a line is a set {(x, y): ax + by = c} where a and b are not both 0).
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what is the value of y when x 3 if the equation of the regression line is y 23.1 - 3.8x ?a. 4.73b. 5.29c. 34.5d.
A sample of 3 is taken from a population of 12 engines. what is the probability that out of 3 taken, at least one is english standard engine?
For the most recent year available, the mean annual cost to attend a private university in the United States was $20,182. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,400.
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you plan to conduct a survey to find what proportion of the workforce has two or more jobs. you decide on the 99
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