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For better readability, I have split off proper map (topology) from proper morphism (general) and added disambiguation. Added classes of examples at proper map.
Added the much needed references:
One of the early reference on proper maps is
A considerable expanded treatment is given in the third edition, see Chapter I, Section 10:
English translation of the 1971 edition:
The localic version of proper maps was introduced by Johnstone:
Peter Johnstone, Factorization and pullback theorems for localic geometric morphisms, Univ. Cath. de Louvain, Sem. de math, pure, Rapport no. 79.
Peter Johnstone, The Gleason cover of a topos, II, Journal of Pure and Applied Algebra 22:3 (1981), 229–247. doi.
Thanks!
have added doi:10.1007/978-3-642-61701-0 for Bourbaki’s book
fixed the link doi:10.1016/0022-4049(81)90100-6 (for “The Gleason cover…”): Since the url has unescaped parenthesis, it does not work with the [link](url)
-syntax, unfortunately. One can escape the parenthesis if one remembers or bothers to look up the respective codes, otherwise one can fall back to HTML syntax <a href="url">link</a>
.
Do we have any hyperlink for
?
Re #10:
In the second paper, Johnstone writes:
Parts of the paper (in particular the contents of Section 1) appeared in a preliminary form in [16]; I am grateful to Francis Borceux for providing me with the incentive to write [16].
where [16] is the paper “Factorization…” and Section 1 is the section about proper maps.
So I think it is safe to say that the “Factorization…” paper is just a preprint that was never properly published (as indicated by “Rapport no. 79”), and its mathematical content relevant to proper maps appeared in Johnstone’s 1981 paper, which was submitted in 1979. So there is really no point in citing the “Factorization…” paper other than to move the priority date a few months back (not that it is under dispute anyway).
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