Hi, I've been studying topology over the last semester and one thing that I was wondering about is why exactly is topology defined the way it is?(adsbygoogle = window.adsbygoogle || []).push({});

For a refresher:

given a set X we define a topology, T, to be a collection of subsets of X with the following 3 properties:

1) the null set and X are elements of T

2) the union of any elements of T is also in T (infinite)

3) the intersection of any of the elements of T is also in T (finite)

I was reading some measure theory and sigma-algebras are defined in a similar way, so I was wondering if someone could shed some light for me.

thanks,

Jordan

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# Definition of topology

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