# open

1. ### Modeling with Functions- open box problem

A graphing calculator is recommended.A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions W = 14 in. by L = 25 in. by cutting out equal squares of side x at each corner and then folding up the sides (see the figure).(a) Find a function that models the...
2. ### Question concerning covering the rationals with open intervals (paradox?)

The following seems paradoxical. Consider the following countable collection of open intervals: I1 is ( 0, 1/2 ), I2 is ( 1/2, 3/4 ), I3 is ( 3/4, 7/8 ), etc. The sum of the lengths of the intervals is 1. Now cover each rational number with one of the intervals. Either 1) two successive...
3. ### We'll have the Open Thread up

New Orleans Saints vs Minnesota Vikings live stream Cincinnati Bengals vs Tennessee Titans live stream Cleveland Browns vs Baltimore Ravens live stream Detroit Lions vs Green Bay Packers live stream Jacksonville Jaguars vs Indianapolis Colts live stream
4. ### Classifying open and closed sets

Hi; let X={1,2,3}. The topology of X is the induced topology from the usual topology on the real line. Consider the product space X * [a,b], where a,b are real numbers. My question is classify all open sets and closed sets of X*[a,b]. what about 1*[a,b], is it open set? thank you in advance
5. ### Open Ended Question

Using each of the numbers 1, 3, 5, 7, and 9 exactly once, create a mathematical expression, containing at least two operations, that has a value greater than 100 and less than 150. Show how the value of your expression is determined.
6. ### Open map theorem

Hello! I wanted to ask something about functional analysis but i looks that this topic doesn't exist. I hope it is ok to publish it here. Well, I wanted to proove that: Let X and Y be two Banach spaces and "f" a map between the, such tahta it is linear, continuous and surjerctive. Then: If K is...
7. ### set theory problem, open and close intervals equivalance

hello there, i am trying to prove a set theory problem relating open and half open intervals. help needed. 1- [0,1] ~ (a,b) 2- [0,1] ~ [a,b) 3- [0,1] ~ (a,b] where a,b belongs to R and ~ is equivalent sign. for question 2, [0,1] ~ [a,b) i have defined a function such that f(x) =...
8. ### increasing, continous function on open interval

My attempt to prove (=>): Fix x in I. Since I is open, there is a ball of radius r>0 about x, so there points on the left and points on the right of x that belong to I. Fix the radius r. f is continuous and monotone on I; continuous and monotone on (x-r, x+r) which is bounded. [Using the...
9. ### Proving (-infinity, 0) is open

Hi, I've done most of the proof(I think), but I'm lost anyone willing to finish it off for me? I've spent a while on it and i'm stuck. Let x be an element of (-infinity, 0) this implies x < 0 chose an r such that abs(r) < abs(x) let y be an element of (x -r, x+r). This implies x-r<y<x+r which...
10. ### Arbitrary intersection of open sets

Arbitrary intersection of the open set (-1/n,1/n) where n is a natural number is zero. Also the arbitrary intersection of the set (-r,r) where r is a positive real numbers is zero. Could someone please explain, why is it like this ?
11. ### Question about open extensions of sets in metric spaces.

Let (X,d) be an arbitrary metric space. For every A\subset X and t>0, we define the open t-extension of A as the set A_t=\{x\in X:d(x,A)<t\}, where d(x,A)=\inf\{d(x,y):y\in A\}. It seems intuitive that, given A\subset X and s,t>0, we should have that A_{t+s}=(A_t)_s=(A_s)_t. However, I...
12. ### Open university text books in PDF format

Is it ok to ask on here about sourcing PDF copies of textbooks? I'm living in Thailand and my books are back in the UK and I was wanting to brush up on my skills to take some more courses. I've completed MU123, MST121, and a part of MS221. I'd love to have copies of the textbooks to look over...
13. ### What is the most economical method to "open", say, 3^4567?

What kind is an algorithm which "opens" large natural base numbers with natural number exponents? Manually 3^5 is easy as it only demands 5 repetitive multiplications (3*3*3*3*3) in order to find precise answer (=243). But 3^4567 does not fit in screen of a typical calculator. Even if we use...
14. ### Open and metric

can someone help me to solve these problems in details?? Consider A =(0,1)× R. Is A open w.r.t. the topology induced by the French railway metric in R2? how about B=(-1,1)× R???
15. ### minimizing the cost of making a box with an open top

a box is made with a square bottom and open top to hold a volume of 8ft3. the material for the sides cost $4 per square foot and the material for the bottom costs$1 per square foot. What dimensions will minimize the cost of the box?
16. ### Markov processes and related semie group (closed, open)

I have a problem to solve it, Markov processes and relationship semie group (closed, open), and I find nothing. I Demende and explaining in Markov is its possible and thank you.
17. ### integral of open set

for part A i assume that f is in norm space C[0,1],||.|| , then choose a sequence fn in C[o,1] s.t fn->f then for 0<fn<1 so 0<f<1 i.e. A is closed i am not sure my answer here for part B i assume the anti-derivatice of f(t) to be K(t)+c therefore, by F(f)=2K(1/2)+1/2-K(1)-K(0) then how should...
18. ### metric space proof open and closed set

show the set {f: ∫f(t)dt>1(integration from 0 to 1) } is an open set in the metric space ( C[0,1],||.||∞） C[0,1] is f is continuous from 0 to 1.and ||.||∞ is the norm that ||f||∞ =sup | f| and if A is the subset of C[0,1] defined by A={f:0<=f<=1} is closed in the norm ||.||∞ norm. first...
19. ### Infimum of integral of open set

I have already done part a and b. Part a is easy, for part b, i let the anti-derivative of f to be k(t)+c and arrive at the answer that F(f)= 1/2+ 2*k(1/2) - k(1). But i don't know how to do the next part, can anyone give me a hint? the question c ask me to show that the infimum of F is 0 and it...
20. ### Open Sets with respect to Different Topologies

Hi, just trying to wrap my head around a few concepts; I've only just started topology so correct me if I'm wrong: is it possible, given a set X with two different topologies, to have a subset of X open with regard to one topology, and not open with regard to the other? And could someone give me...