Recent content by math25

you are right, thanks

Find two open sets A and B, such that A is subset of B, A is not equal to B, and m(A)=m(B) Can I use these two sets? A=(0,2) B=(0,1) U (1,2) thanks

Would this proof work? let r=1/n for n=1,2,3... and {In, n in N where In is the set corresponding to r=1/n, that is In is a maximal set having the property that is greater then or equal to 1/n for any a,b in In Let W =Un In since W is the union of countably many countable sets, W is...

Well, the rational numbers are countable, so any open set in R is the countable union of components. But I am not sure how to write a proof...

Sorry, this is what I have before problem: Let A be an open subset of the interval [0; 1]. Our goal is to show that A =the union In where for all n in N, In is a possibly empty open interval and for all n and k in N, if n is not equal to k then In intersect Ik = empty set We begin by defi...

Hi, can someone please help me with this problem. Let A be an open subset of the interval [0; 1]. 1. Show that the set W = {C(x) : x is in A} is countable or finite. This is what I have... Suppose W is an infinite subset of N. Then we have f : W-> N, which is one-to-one. By the fact that...

Hi, can someone please check if my proof is correct 1. a) Assume f : R -> R is continuous when the usual topology on R is used in the domain and the discrete topology on R is used in the range. Show that f must be a constant function. My attempt : Let f: R --> R be continuous. Suppose...

agree, I"ll be working on it today...

It was mistake, which I corrected later...it converges to 0 not 1.

thank you so much... It seems like I wrote everything wrong, for the second sequence that's what I meant to say, and I've already proved it. for the first sequence, it converges to 0 in usual topology and this is what I have so far... For every open U s.t. 0 is in U, there exist N such...

hi, can someone please help me with this problem. Let T be the collection of all U subset R such that U is open using the usual metric on R.Then (R; T ) is a topological space. The topology T could also be described as all subsets U of R such that using the usual metric on R, R \ U is...

Well, before I thought it wasn't, but I am not sure anymore...it seems like it is... c) and d) are Hausdorff, therefore metrizable, right?

thanks, what do you think about b) please see the post above yours

Actually, I think a) is not metrizable because it is not Hausedorff ? Also, for b) the cocountable topology is not Hausedorff therefore b) is not metrizable?

they are always Hausdorff ? Am I right for e) a) and b) ?