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Sep 1 at 10:36 comment added Ali Taghavi @PietroMajer BTW no because bounded intervals are not algebraic equivalent to unbounded intervals for example $(0,1)$ is not algebraic equivalent to some thing $(0,\infty)$. So I prefer the original formulation: arbitrary open sets $U,V$
Sep 1 at 10:10 comment added Ali Taghavi @PietroMajer Yes we may assume $U=V=(0,1)$
Sep 1 at 5:22 comment added Pietro Majer U and V then should be open intervals, wlog (0,1) no ?
Aug 31 at 22:22 history edited Ali Taghavi CC BY-SA 4.0
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Aug 31 at 22:02 history edited Ali Taghavi CC BY-SA 4.0
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Aug 31 at 21:56 history asked Ali Taghavi CC BY-SA 4.0