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Timeline for Non meager rectangle

Current License: CC BY-SA 3.0

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Jun 16, 2015 at 10:35 vote accept Ashutosh
Jun 15, 2015 at 21:34 comment added Nate Eldredge To see how the quoted result implies a solution to the given question (just because it took me a couple minutes): take $X = \mathbb{R}$ and $E = \mathbb{R}^2 \setminus G$, apply the quoted result to produce $F$; then $F \times F \subset G \cup D$, where $D$ is the diagonal. Now let $U,V$ be any two nonempty disjoint open subsets of $\mathbb{R}$; take $A = F \cap U$ and $B = F \cap V$. Since $F$ is nowhere meager, $A,B$ are nonmeager. We have $A \times B \subset F \times F \subset G \cup D$, and since $A,B$ are disjoint, we have $A \times B$ disjoint from $D$. So $A \times B \subset G$.
Jun 15, 2015 at 20:33 history edited Alex Ravsky CC BY-SA 3.0
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Jun 15, 2015 at 20:31 history rollback Alex Ravsky
Rollback to Revision 2
Jun 15, 2015 at 20:30 history rollback Alex Ravsky
Rollback to Revision 3
Jun 15, 2015 at 20:24 history rollback Alex Ravsky
Rollback to Revision 2
Jun 15, 2015 at 20:21 history edited Alex Ravsky CC BY-SA 3.0
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Jun 15, 2015 at 20:15 history edited Alex Ravsky CC BY-SA 3.0
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Jun 15, 2015 at 19:22 history answered Alex Ravsky CC BY-SA 3.0