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topological_space [2015/02/26 20:24]
nikolaj
topological_space [2015/02/26 20:24] (current)
nikolaj
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 A comment on the intersection axiom requiring finiteness: A major motivation for topological spaces is $\mathbb R^n$ with the sets "open ball" and in this setting, an infinite intersection of open sets need not be open. E.g. consider the set of open intevals $(-\tfrac{1}{n},​\tfrac{1}{n})$. A comment on the intersection axiom requiring finiteness: A major motivation for topological spaces is $\mathbb R^n$ with the sets "open ball" and in this setting, an infinite intersection of open sets need not be open. E.g. consider the set of open intevals $(-\tfrac{1}{n},​\tfrac{1}{n})$.
  
-==== Reference ​====+=== Reference ===
 Wikipedia: [[http://​en.wikipedia.org/​wiki/​Topological_space|Topological space]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Topological_space|Topological space]]
  
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