Real Analysis : Open Intervals

Please help with the following problem. Use the following steps to prove that every non-empty open subset of R is a union of at most countably many disjoint open intervals. Suppose that G is a non-empty open subset of R. 1. For each a <- G let Ia be the union of all those open intervals I which contain a and are containe

Prove that the open interval (-pi/2,pi/2) considered as a subspace of the real number system, topologically equivalent to the real number system. Prove that any two open intervals, considered as subspaces of the real number system, are topologically equivalent. Prove that any open interval, considered as a subspace of the r

Show that the class of all finite unions of closed-open intervals on the real line is a ring of sets but is not a Boolean algebra of sets.

Show that the class of all finite unions of closed-open intervals on the real line is a ring of sets but is not a Boolean algebra of sets.

Convert each z interval to x interval a) -2.17

Which of the following topological spaces is normal? a) Reals with the "usual topology." b) Reals with the "finite complement topology:" U open in X if U - X is finite or is all of X. c) Reals with the "countable complement topology:" U open in X if X - U is countable or is all of X. d) Reals with the "lower limit topolog

Let f(x)=x^(4)â?'6x^(3)+12x^(2). Find (a) the intervals on which f is increasing, (b) the intervals on which f is decreasing, (c) the open intervals on which f is concave up, (d) the open intervals on which f is concave down, and (e) the x-coordinates of all inflection points. (a) f is increasing on the interval(s) = (b)

My questions are from sections 5 and 6. Since most of questions are from section 6, I will just just attach reference_6 pdf file with my question sheet. I think you actually have all of my reference copies. This is the same on-line link to my textbook that I sent you earlier today: http://books.google.com/books?id=z8IaHg

Real Analysis Let and let be continuous map given by .