Wednesday, June 6, 2018

general topology - Show that f is not continuous at a?

Let aR and f:RR be defined by f(x)=1 when x>a, and otherwise f(x)=0. Show that f is not continuous at a.



This problem is in a section on open balls and neighborhoods. I can show that it's continuous every where other than a, but I can't think of a reason it wouldn't be continuous at a.

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