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In distillation, THE CUT-POINT is the boiling point of the pseudo-component which is equally divided over distillate and bottom product.

This article is or was the subject of a Wiki Education Foundation-supported course assignment. Further details are available on the course page. Student editor(s): Chen.shuj.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 18:52, 16 January 2022 (UTC)[reply]

I basically expand the article using information both in the original reference "General Topology" by Willard and other two articles I have found. I also reorganize the sections a bit. I couldn't find many examples about this, most of examples of cut-points are just in combination of lines. Hopefully, someone could add some interesting examples. Also, it would be great if anyone can find some additional sources. I can only find these many helpful to me.Chen.shuj (talk) 03:08, 9 April 2016 (UTC)[reply]

The Khalimsky line is an interesting example of a cut point space. And it satisfies the interesting theorem that no proper subspace of it is a cut point space, and it is the only space with that property. Note however that the terminology "irreducible cut-point space" is not "notable" (WP:N) for wikipedia. It was just the terminology used locally in one paper (Honari-Bahrampour) to give a name to the concept, but once the result is proved that there is only one representative in this class of topoological spaces, namely the Khalimsky line, the concept itself loses any interest. The result is interesting though and should be there. I intend to correct this and rephrase things without mention of "irreducible cut-point space" in the near future. PatrickR2 (talk) 01:11, 20 December 2024 (UTC)[reply]

The cleanup has now been made. PatrickR2 (talk) 06:16, 19 August 2025 (UTC)[reply]