Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Show that {x} are open sets in X for all points x∈X, then all subsets of X are also open in X.
 one year ago
 one year ago
Show that {x} are open sets in X for all points x∈X, then all subsets of X are also open in X.
 one year ago
 one year ago

This Question is Closed

experimentXBest ResponseYou've already chosen the best response.1
{x} collection of open sets ... open covering of X?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
looks like i am not understanding the Q ... you sure the Q is right?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
any background on the Q? for some reason I find point set topology very hard.
 one year ago

waltersBest ResponseYou've already chosen the best response.0
what i know that the set is open when all its point are interior
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
But discrete points are itself closed set.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
where does this problem come from (book) ??
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
which book are you using as Text Book ??
 one year ago

waltersBest ResponseYou've already chosen the best response.0
RG Bartle and DR Sherbert ,introduction to real analysis john wiley &sons
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
@walters have you managed to go all though chapters to reach Point Set Topology at the end?
 one year ago

waltersBest ResponseYou've already chosen the best response.0
not really but i think his question is open and closed sets
 one year ago

waltersBest ResponseYou've already chosen the best response.0
i understand it this way but i can't show it dw:1361566625628:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
Let F be collection of A's ... and \( X = \cup_{A \in F} A\) and \( B(x;r) \subset A_i \forall x \in A, \implies B(x;r) \subset X\) shows that X is open set.
 one year ago

waltersBest ResponseYou've already chosen the best response.0
"compact "what do u mean
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
I think what you are doing is Let X be a closed set, and \( x \in X \) be a point in X. and \( X  {x}\) is a subset of X which is open in X. let me ask others.
 one year ago

waltersBest ResponseYou've already chosen the best response.0
is what i am thinking "but not quit sure"
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
let me ask experts ... I'll reply you in sometime.
 one year ago

waltersBest ResponseYou've already chosen the best response.0
i think since the subset of X are open this also implies that {x}and its complements are also open
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
i got the hint: in the discret topology all points are open
 one year ago

waltersBest ResponseYou've already chosen the best response.0
so does this mean that there is no relationship between {x} and its complement
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
no ... use the fact that union of infinite number of open sets is and open set.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
or simply just union of open sets.
 one year ago

waltersBest ResponseYou've already chosen the best response.0
i mean like "ie if {x} is open it does not imply that its complement is also closed "
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
I guess not in discrete topology
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1361569963336:dw usually we have neither closed nor open set.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
but in discrete topology we seem to have http://mathworld.wolfram.com/DiscreteSet.html http://mathworld.wolfram.com/DiscreteTopology.html
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
the neighborhood of the boundary will not contain any point of that inner set, which makes the compliment open.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
as to your question, the subsets of X will be power sets of its elements which are open. And the union of open set is open. Hence all the subsets will be open.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
P.S. I am not sure, I don't have experience with Topology.
 one year ago

phiBest ResponseYou've already chosen the best response.0
I am an engineer, and have not studied analysis.
 one year ago

waltersBest ResponseYou've already chosen the best response.0
@JamesJ and @KingGeorge
 one year ago

waltersBest ResponseYou've already chosen the best response.0
dw:1361653147330:dw i think they mean it this way because of the question
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.