Thomas E.
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 Jun 12 comment Collection of converging sequences determines the topology? @BrianM.Scott: You define $\tau_{2}$ by using the notion of $X$ and $D$ simultaneously. That is the reason why I'm asking. Jun 12 comment Collection of converging sequences determines the topology? What role does $X$ play in the above construction. Is $D\subset X$? Jun 12 revised Collection of converging sequences determines the topology? added TeX. Jun 12 suggested approved edit on Collection of converging sequences determines the topology? Jun 12 comment Vitali set of outer-measure exactly $1$. The person who down-voted is welcome to leave a comment and explain why so. Jun 12 asked Vitali set of outer-measure exactly $1$. Jun 12 revised Interior, exterior and boundary of sets in $\mathbb R^2$ added 10 characters in body Jun 12 comment Interior, exterior and boundary of sets in $\mathbb R^2$ Your answer on $B$ is not correct. Jun 12 answered Interior, exterior and boundary of sets in $\mathbb R^2$ Jun 12 comment Limits of Subsequences With the same idea it actually follows that for any subsequence of $\{t_{n}\}$ we find such a subsequence of $\{s_{n}\}$ that decreases more rapidly. And I don't think we needed the fact that $s_{n}\leq t_{n}$ at all. Jun 12 comment subsets probability question What have you tried so far? And is this a homework? Jun 11 comment True if sigma-compact @SamL.: Thank you. Jun 11 answered True if sigma-compact Jun 11 comment Form of $\sigma(X_n)$ and $\sigma(X_n)$-measurability @Justin: Topology is just the family of open sets. If it confuses you, you can ignore that part and simply think of $\mathscr{B}(X)$ being the Borel $\sigma$-algebra of $X$ the way you have it defined. Jun 11 comment True if sigma-compact Found it now. And it's true that this is very questionable since no proof is given. If $X$ is $\sigma$-compact then the Lemma is true, as $E$ is a countable union of Borel sets. Let me see if I'm able to do something with the locally compact Hausdorff case. Jun 11 comment True if sigma-compact I couldn't find this Lemma from Royden's book. What page is it? Jun 11 comment is there any one one and onto function from $A$ to $B$ That is correct. Jun 11 comment is there any one one and onto function from $A$ to $B$ You could start by writing down the sets $A$ and $B$ in simpler forms. They are both open intervals. Jun 11 comment True if sigma-compact What do we know about the topology of $X$? Jun 11 revised Form of $\sigma(X_n)$ and $\sigma(X_n)$-measurability added 1 characters in body