Timeline for Non meager rectangle
Current License: CC BY-SA 3.0
9 events
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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
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Jun 15, 2015 at 20:30 | history | rollback | Alex Ravsky |
Rollback to Revision 3
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Jun 15, 2015 at 20:24 | history | rollback | Alex Ravsky |
Rollback to Revision 2
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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 |