8:32 AM
specific-question Maybe the tag elementary-theory-category-of-sets would be suitable here: Elementary theory of the category of relations?
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Has anyone ever attempted to write down axioms capturing the behaviour of ${\bf Rel}$, the category of relations? Lawvere's ETCS attempts to axiomatize the behaviour of the subcategory ${\bf Set}$ of ${\bf Rel}$ and ends up with a theory equiconsistent with $ZF-Replacement$; I'm curious if axio...
1 hour later…
9:37 AM
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Nancy Dykes says in the proof of Theorem 3.4 in her article Generalizations of realcompact spaces that by a result of John Mack, if for every $p\in \beta X\setminus X$ there exists a nonnegative upper semicontinuous function $f$ on $\beta X$ such that $f$ is positive on $X $ and $f\left( p\right)...
In mathematics, in the field of topology, a topological space is said to be realcompact if it is completely regular Hausdorff and every point of its Stone–Čech compactification is real (meaning that the quotient field at that point of the ring of real functions is the reals). Realcompact spaces have also been called Q-spaces, saturated spaces, functionally complete spaces, real-complete spaces, replete spaces and Hewitt–Nachbin spaces (named after Edwin Hewitt and Leopoldo Nachbin). Realcompact spaces were introduced by Hewitt (1948).
== Properties ==
A space is realcompact if and only if it...
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