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Show that the standard topology on Q is not the discrete topology.
Solution
It is not discrete since p/q is not open
it it was then p/q = U intersection Q for some open set U is a subset of R
But since this is not possible , because the rational number are dense, so any open ball contains
infinitely many of them

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Show that the standard topology on Q is not the discrete topology..pdf

  • 1. Show that the standard topology on Q is not the discrete topology. Solution It is not discrete since p/q is not open it it was then p/q = U intersection Q for some open set U is a subset of R But since this is not possible , because the rational number are dense, so any open ball contains infinitely many of them