Timeline for Image of the Hilbert space under a continuous bijection
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3 events
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| Oct 8, 2011 at 4:32 | comment | added | Will Sawin | It doesn't seem like there's much more to say. No traditional topologies on vector spaces that I am aware of are coarser than the standard one and metrizable. For $\mathbb R^n$, the only thing you can do is 6: glue paths to infinity to points nearby. Locally (compactly), the topology is preserved. In Hilbert space, you can do all kinds of crazy stuff, but the only thing that's both consequential and admits comprehensible description (that I am aware of) is the 6 thing again. | |
| Oct 7, 2011 at 12:29 | comment | added | Igor Belegradek | @Will Sawin: thanks for thinking about this, but aren't you just restating my question? I wish to have some examples of spaces that can (or cannot) appear as $Y$, and I am not sure how to use your answer for the purpose. | |
| Oct 7, 2011 at 3:52 | history | answered | Will Sawin | CC BY-SA 3.0 |