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Nov 4, 2010 at 9:50 comment added HenrikRüping There is a problem. Property (3) needn't be satisfied. (Consider the Cantor set and let $C_0$ be the right half and $C_1$ the right half of the left half etc. then the $lub$ of this family is the whole space. It is not the lowest upper bound of any finite subfamily.
Nov 3, 2010 at 16:03 history edited HenrikRüping CC BY-SA 2.5
typo; added 7 characters in body
Nov 3, 2010 at 15:46 history edited HenrikRüping CC BY-SA 2.5
added 23 characters in body; added 4 characters in body
Nov 3, 2010 at 15:40 history answered HenrikRüping CC BY-SA 2.5