From what I understand is that its because I can always chose some r such that the distance between $|x-x_0|\ \leq r$ is always in the set, intuitively what does this mean? because the positive semi-definite set is closed, I cant do the same thing? I am guessing its because for PD sets the boundary is not in the set? while 0 is for PSD sets. A formal proof would help.
2026-03-29 11:42:57.1774784577
How to prove the positive definite set is open?
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