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Oct 14, 2011 at 7:24 comment added Shripad Thank you Terry for the explanation. Now I guess I understand the modifier "locally" better.
Oct 14, 2011 at 7:23 vote accept Shripad
Oct 13, 2011 at 18:57 comment added André Caldas This is a very neat way to justify my intuitive but not so elaborate and well justified belief that any neighborhood should have the property. Note taken! :-) I think of a neighborhood as a "sufficiently large set". Large enough to be considered a neighborhood. Often, one needs to choose a "small" set, but at the same time, big enough to make the small step big enough to achieve the goal... "path connect two points", for instance.
Oct 13, 2011 at 16:38 history edited Terry Tao CC BY-SA 3.0
added 119 characters in body; added 2 characters in body; added 157 characters in body
Oct 13, 2011 at 16:32 history answered Terry Tao CC BY-SA 3.0