The term comes up in a paper here https://arxiv.org/pdf/0706.3560.pdf bottom of page 4.
I haven't found any explanation for this with Google or the textbooks available to me.
2026-04-03 14:50:27.1775227827
What is an "Honest" Accumulation Point?
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I think it's just an ad hoc, colloquial term they introduce (but not reuse) to distinguish it from the first type they just discussed, and which they consider "boring" or "trivial" in some sense. That's how I read it. Don't look for any deep technical meaning...