Functionally compact spaces,C-compact spaces and mappings of minimal Hausdorff spaces

Modal compact Hausdorff spaces

We introduce modal compact Hausdorff spaces as generalizations of modal spaces, and show these are coalgebras for the Vietoris functor on compact Hausdorff spaces. Modal compact regular frames and modal de Vries algebras are introduced as algebraic counterparts of modal compact Hausdorff spaces, and dualities are given for the categories involved. These extend the familiar Isbell and de Vries d...

Subordinations, closed relations and compact Hausdorff spaces

We introduce the concept of a subordination, which is dual to the well-known concept of a precontact on a Boolean algebra. We develop a full categorical duality between Boolean algebras with a subordination and Stone spaces with a closed relation, thus generalizing the results of [14]. We introduce the concept of an irreducible equivalence relation, and that of a Gleason space, which is a pair ...

Reduced Coproducts of Compact Hausdorff Spaces

By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usu...

On Compact Hausdorff Spaces of Countable Tightness

A general combinatorial theorem for countably compact, noncompact spaces is given under the Proper Forcing Axiom. It follows that compact Hausdorff spaces of countable tightness are sequential under PFA, solving the Moore-Mrowka Problem. Other applications are also given.

Topology Proceedings 9 (1984) pp. 243-268: BETWEEN MINIMAL HAUSDORFF AND COMPACT HAUSDORFF SPACES