Timeline for Does every separated measurable space embed into a power of $\{0,1\}$?
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| Feb 28, 2014 at 19:24 | comment | added | Tobias Fritz | That's precisely what I had tried initially (see the original version of my question). If you know about Gelfand duality and Stone duality, it seems like a natural thing to try and indeed the resulting injective function is measurable (with respect to the Baire, and hence also the Borel $\sigma$-algebra on $\{0,1\}^\Sigma$). However, I don't see why this function should also take measurable sets to measurable sets, and I think this fails in general. In fact, I suspect that its image may not even be measurable, but I don't have a concrete example of that. | |
| Feb 28, 2014 at 14:39 | history | answered | Gerald Edgar | CC BY-SA 3.0 |