no , since there is a function which lsc but not usc.
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yes it is a continuous function.
An infinite sum of continuous functions does not have to be continuous. For example, you should be able to construct a Fourier series that converges to a discontinuous function.
It is a trigonometric function. It is also continuous.
No, they can only be jump continuous.
Not at all.Y = x2 is a continuous function.