These conditions are separation axioms that are somewhat stronger than the more familiar Hausdorff axiom T 2.
2.
;Quasicompact : See "'Hausdorff separation axiom, and they use the term "'quasicompact "'to mean what we call in this glossary simply " compact " ( without the Hausdorff axiom ).
3.
Like the other axioms of countability, separability is a " limitation on size ", not necessarily in terms of cardinality ( though, in the presence of the Hausdorff axiom, this does turn out to be the case; see below ) but in a more subtle topological sense.
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