Does right continuity imply only countably many discontinuities? That is, if $f:\mathbb{R}\rightarrow \mathbb{R}$ is right continuous then does it only have countable many discontinuities?
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Have you thought about it? – Pedro May 22 '14 at 03:26
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1Yes, for the standard reason: Show that any discontinuity is a jump discontinuity. Show how this allows you to assign (injectively) an open interval to each discontinuity, and conclude. – Andrés E. Caicedo May 22 '14 at 03:27
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1You can also see this thread: http://math.stackexchange.com/questions/65941/if-f-mathbbr-to-mathbbr-is-a-left-continuous-function-can-the-set-of-disc – Batman May 22 '14 at 03:28
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Ok thanks guys. – user30201 May 22 '14 at 03:41