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neighbourhood [2014/10/25 14:47]
nikolaj old revision restored (2014/10/25 14:22)
neighbourhood [2014/10/25 14:47] (current)
nikolaj old revision restored (2014/10/25 14:25)
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 === Predicates === === Predicates ===
 Consider $X$ together with a topology, then Consider $X$ together with a topology, then
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-//Hausdorff space// means you can separate Neighbourhoods:​ 
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-| @#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 $\mathbb R^n$:
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 === 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]]
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