So I am pursuing my master's degree in mathematics and doing a course on Fourier series i encountered piecewise continuous functions. From the definition it seems that they must be bounded functions as on each subinterval the limits from both sides must exist. But i'm still not sure whether they are bounded or not. I did come across a problem in the book by N.H Asmar that seemed to consider bounded different from piecewise continuous. Anyway please clarify the relation between piecewise continuous and boundedness. According to me a piecewise continuous function should be bounded.
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Why do you think the limits from both sides must exist? Perhaps you could cite here the exact definition of piecewise continuous that you are using. What about $f(x)=1/x$? – Jukka Kohonen Sep 04 '21 at 16:04
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Yeah, I suppose that piecewise continuous implies that one sided limits exist – LL 3.14 Sep 05 '21 at 19:57