Looking for a reference on the observation that the set of stable matchings form a distributive lattice. This is attributed to Conway by Knuth in "Marriages Stables" but I would like an explicit reference if possible, likely a text book. An undergrad student needs it for his bibliography in a ter...

Is $[0,1]$ a disjoint union of $\aleph_1$ compact subsets with empty interior? The answer is obviously yes assuming the continuum hypothesis. Also, by Baire's lemma, the answer is negative if one replaces $\aleph_1$ with $\aleph_0$. Does anybody know if this question has a definite answer o...

In the book Infinite abelian groups Vol. I by L. Fuchs, on page 154, the notion of the generalized $p$-height of an element in an abelian group is defined, as follows: Let $A$ be an abelian group and let $p$ be a prime number. First we define for every ordinal $\sigma$ a subgroup $p^\sigma A$ o...

For the (Hausdorff) compact spaces I can think of, compactness is established either using a product of compact spaces (including the Heine-Borel Theorem, the Banach-Alaoglu Theorem, Stone-Čech compactification, etc.) or by inheriting compactness from another space (e.g. the Hausdorff metric on c...