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Oct 13, 2011 at 22:05 comment added David White For all points p and for all neighborhoods U there is a smaller neighborhood V satisfying the property. I think this is the standard for every locally <blank> other than locally compact
Oct 13, 2011 at 20:20 history edited André Caldas CC BY-SA 3.0
Fixed math statement.
Oct 13, 2011 at 14:52 comment added André Caldas Which one is your "standard 'locally <blank>' definition"? :-)
Oct 13, 2011 at 13:58 comment added David White Wow, I never knew this! I always figured the strange definition was to give nice properties, but in fact the nice properties are all for locally compact Hausdorff spaces (e.g. they are characterized by being open subspaces of compact Hausdorff spaces), so I'm guessing point-set topology courses everywhere could just use the standard "locally <blank>" definition and avoid this confusion completely.
Oct 13, 2011 at 4:01 history answered André Caldas CC BY-SA 3.0