# Differences

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 neighbourhood [2014/10/25 14:25]nikolaj neighbourhood [2014/10/25 14:47]nikolaj old revision restored (2014/10/25 14:22) Both sides previous revision Previous revision 2014/10/25 14:47 nikolaj old revision restored (2014/10/25 14:25)2014/10/25 14:47 nikolaj old revision restored (2014/10/25 14:22)2014/10/25 14:25 nikolaj 2014/10/25 14:25 nikolaj old revision restored (2014/10/25 14:22)2014/10/25 14:23 nikolaj 2014/10/25 14:22 nikolaj 2014/03/21 11:11 external edit2013/09/14 16:42 nikolaj 2013/09/14 16:41 nikolaj 2013/09/14 16:38 nikolaj 2013/09/14 16:37 nikolaj 2013/09/14 16:37 nikolaj 2013/09/14 16:37 nikolaj 2013/09/14 16:35 nikolaj 2013/09/14 16:32 nikolaj 2013/09/14 16:30 nikolaj 2013/09/14 16:20 nikolaj 2013/09/14 16:00 nikolaj 2013/09/14 16:00 nikolaj 2013/09/14 15:59 nikolaj created 2014/10/25 14:47 nikolaj old revision restored (2014/10/25 14:25)2014/10/25 14:47 nikolaj old revision restored (2014/10/25 14:22)2014/10/25 14:25 nikolaj 2014/10/25 14:25 nikolaj old revision restored (2014/10/25 14:22)2014/10/25 14:23 nikolaj 2014/10/25 14:22 nikolaj 2014/03/21 11:11 external edit2013/09/14 16:42 nikolaj 2013/09/14 16:41 nikolaj 2013/09/14 16:38 nikolaj 2013/09/14 16:37 nikolaj 2013/09/14 16:37 nikolaj 2013/09/14 16:37 nikolaj 2013/09/14 16:35 nikolaj 2013/09/14 16:32 nikolaj 2013/09/14 16:30 nikolaj 2013/09/14 16:20 nikolaj 2013/09/14 16:00 nikolaj 2013/09/14 16:00 nikolaj 2013/09/14 15:59 nikolaj created Last revision Both sides next revision Line 11: Line 11: === Predicates === === Predicates === Consider $X$ together with a topology, then Consider $X$ together with a topology, then + + //Hausdorff space// means you can separate Neighbourhoods:​ + + | @#EEEE55: predicate ​  | @#EEEE55: $X$ ... Hausdorff space $\equiv \forall (x,y\in X).\ x\neq y \implies \exists ​ (U_x\in\mathrm{Neighbourhood}(x),​ U_y\in \mathrm{Neighbourhood}(y)).\ U_x\cap U_y=\emptyset$ | //locally euclidean space// means $X$  is homeomorphic to $\mathbb R^n$: //locally euclidean space// means $X$  is homeomorphic to $\mathbb R^n$: Line 22: Line 26: === Reference === === Reference === Wikipedia: ​ Wikipedia: ​ + [[https://​en.wikipedia.org/​wiki/​Neighbourhood_%28mathematics%29|Neighbourhood]],​ [[http://​en.wikipedia.org/​wiki/​Hausdorff_space|Hausdorff space]], [[http://​en.wikipedia.org/​wiki/​Hausdorff_space|Hausdorff space]], [[http://​en.wikipedia.org/​wiki/​Topological_manifold|Topological manifold]] [[http://​en.wikipedia.org/​wiki/​Topological_manifold|Topological manifold]]