I am learning about the para-compact space and nearly para-compact space. I know that every nearly para-compact space is para-compact space but the converse is not true in general. So i need an example of para-compact space which is not nearly para-compact space.
2026-03-27 14:03:34.1774620214
Show that every paracompact space is nearly paracompact but the converse is not true
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You have it backwards: every paracompact space is nearly paracompact, but there are nearly paracompact spaces that are not paracompact. One of them is the space that I described in this answer. Since it is Hausdorff but not regular, it is not paracompact. The proof that it is nearly paracompact is virtually identical to the proof that it is nearly compact.