Union Definition and 229 Threads

Homework Statement Conjecture: If K=a union of subsets of G with K open then each subset in the union is open The Attempt at a Solution Can't really see the proof. In fact it's false as any non discrete topology have open sets which are a union of subsets whch may not be open.

Homework Statement If you have a collection of disjoint open sets in a general topological space whose union is open, is it true that each of them individually must be open? Why? EDIT: this makes absolutely no sense. here is what I meant to ask: EDIT:If you have a collection of disjoint sets...

[SOLVED] Union and Intersection of sets Homework Statement a) Find: \bigcup_{i=1}^{\infty}} A_i b) Find: \bigcap_{i=1}^{\infty}} A_i Where A_i = (0,i), that is, the set of real numbers x with 0 < x < i I was doing okay when they gave me A_i = {i, i+1, i+2, ...}, but now that...

Homework Statement a) Find: \bigcup_{i=1}^{\infty}} A_ib) Find: \bigcap_{i=1}^{\infty}} A_i Where A_i = (0,i), that is, the set of real numbers x with 0 < x < i I was doing okay when they gave me A_i = {i, i+1, i+2, ...}, but now that they're giving me (0,i), and introducing x, I'm getting...

they have an engineering school there and i was wondering what people in academia/industry thought of it.

[b]1. The problem statement, U= x:xless than 11, [b]2. Homework Equations ----(A n B')' n C The Attempt at a Solution

Again, my method of proof is far too messy. Let E be a open subset of R. Any collection of disjoint segments in R must be at most countable - pick one rational in each segment and from there we see that the collection of sets can be mapped to a subset of a countable set. In other words any...

Homework Statement I'm trying to prove that the boundary of the union of two sets is a subset of the union of the boundaries of the two sets. i.e. Show that B(X u Y) c= B(X) u B(Y). Homework Equations The Attempt at a Solution Since I didn't know what to do here, I used the...

Their live concert (basis for their live CD) is going to be broadcast on PBS at 9:00 eastern tonight. If you haven't seen this, please try to tune in. Every one of the band members is stellar, and Jerry Douglas (on dobro) will floor you.

Does <1,x> = <1> U <x> where U denotes union in Z[x] It should be yes because what else could it be?

Hey, Just a tiny question, what is the space called: Reals union infinity?

Awesome tool! My favorite: "marriage" 2001: 2 2002: 0 2003: 1 2004: 9 (election year) 2005: 2 2006: 1 2007: 0edit: stupid! I forgot to post the link: http://www.nytimes.com/ref/washington/20070123_STATEOFUNION.html

Please help me with this. Let be two functions of x, B(x) and A(x). Boas ("A primer or real functions", p. 137) says: If A(x) < B(x), there are rational numbers r and R such that A(x) < r < R < B(x) (OK). Since there are only countable many pairs of rational numbers (OK), the set where...

Is this infinite union closed, open or neither? What is your reason?

I'm trying to show that this set is compact {0} union {2^-m + 2^-n} where n,m are integers and m is less than n I'm thinking that since it's bounded below by 0 and the set contains it's bound that if I can show that it's closed and bounded above that will be a proof but I'm not really...

I brew beer as a hobby and in order to avoid the cold i want to take my boiling inside. Because propane inside my apartment is dangerous I was looking to heat my boil with a modified electric heating element from a hot water heater. I need to figure out an equation that will tell me how...

G'day, I saw very little of the address. From the little I watched he made plenty of 'this or that' statements, I believe were designed to garner bipartisan support to get 'things' done in his waning time left in office. Maybe its me but his demeanor seemed disingenuous, the...

How do you do this proof? Isn't it already obvious given the definition? I have no idea how to go about writing it down. :confused: If someone could help me with this, I would really appreciate it. Thanks :) Sorry I had to write it in such a messy way. Define the closure of A as A closure =...

In reading D. Bohm "Quantum Theory" (1979), on p. 625 he makes the statement..."without appeal to a classical level, quantum theory would have no meaning". And then ..."quantum theory presupposes the classical level and the general correctness of classical concepts in describing this level...

is it true that: \partial(A\cup B) = (\partial(A)\cap \mbox{int}(X-B))\cup (\partial(B)\cap \mbox{int}(X-A)) ? (where \partial(A) is the boundary of A, int(A) is the interior, and A and B are two subsets of the topological space X) I can prove that: \partial(A\cup B) \subset...

Well hello i have a lots of russian books translated in english by mir publishers i am really fond of them they are quiet good. irodov being best in undergrad physics numericals. now i want to know that since these books were written at time of existence of soviet union and the copyright...

"The collapse of Soviet Union hit World's Science and Technology Development hard." What do you think of this remark?

Hey, has anyone seen the applause sign in the congress? :smile: This is more like a pep rally with a string of soundbites!

Carefully base your answers with arguments, because turkey is four decades that is waiting for an answer? what will be the impacts of this new event towards, the European union?

Would you please tell me how "popular" it is today ? I mean if you are still using it in programming or not, since I have heard from many friends of mine that they don't use it at all, even once...So, how about you ? Your ideas are all appreciated, and thank you very much for your help..:sm:

Bravo Europe Union, Shame on you France, Damn the Chinese are smooth... http://news.bbc.co.uk/2/hi/europe/3637807.stm Good Job to the EU for standing ground on true human rights and democracy. Shame on France (and Germany to an extent) for looking to cash in on the Humanitarian crisis...

the UUI demands either jobs or $100 / month in unemployment insurance. 65% of Iraq is unemployed since the war. Iraqis are educated and skilled people who are decended from the inventors of the number zero and the concept of infinity. Why not * cancel the no-bid contracts and put he Iraqi...

Hello, I am having trouble interpreting the definition of the union of two sets as given in Modern Abstract Algebra in Schaum's Outlines. I can see by example but I can't seem to interpret the definition. Could someone reword this for me or give me another spin on this definition? Thankyou...

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