Answer by Daniel Picazo Ezquerra for Proof that if A and B are connected...
Thanks, everybody! I've glanced over your proof in order to not give myself any revealing details and just get the gist of it. As far as I know now, this is the proof:Firstly, to prove the $\Leftarrow$...
View ArticleAnswer by Nuffie for Proof that if A and B are connected sets, $A \cup B$ is...
The proof kinda depends on what (equivalent) definitions of closure and connectedness you've covered. Since you already mentioned that you want to try again with the excellent advice of the commenters,...
View ArticleAnswer by Kraken for Proof that if A and B are connected sets, $A \cup B$ is...
(For the statement to be correct, we need to assume that $A$ and $B$ are both nonempty.)By definition, $A \cup B$ is disconnected iff there are 2 disjoint nonempty open subsets (!) $X,Y$ of $A \cup B$...
View ArticleProof that if A and B are connected sets, $A \cup B$ is connected iff $(\bar...
The problem says: Let $(X,\tau)$ be a topological space so that $A,B \subset X$ are connected sets in said space.For $M\subset X, \bar M$ refers to the closure of $M$.Prove that $A \cup B$ is connected...
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