# Differences

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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]] | ||