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Let $f(x)=\|x\|^2$ in Hilbert space into positive real numbers space I try to prove the $f$ is continuous by the theorem that say $f$ is continuous iff it upper semicontinuous and lower semicontinuous, I want a hint to prove it.

N math
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    Possible duplicate of Why are norms continuous? – freakish Feb 12 '19 at 11:21
  • Welcome to MSE. Your questions lacks details and context. Why are you interested in this question and what have you tried so far? You can find some remarks about how to ask a good question here: https://math.stackexchange.com/help/how-to-ask Also try to use MathJax to increase the readability of your question. –  Feb 12 '19 at 11:22
  • Thank you I see it but if f(x) equal sequar of norm x – N math Feb 13 '19 at 05:11

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