Embeddings into pseudocompact spaces of countable tightness

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.

Products of ¿-spaces and Spaces of Countable Tightness

In this paper, we obtain results of the following type: if /: X -» Y is a closed map and X is some "nice" space, and Y2 is a &-space or has countable tightness, then the boundary of the inverse image of each point of Y is "small" in some sense, e.g., Lindelöf or «¿¡-compact. We then apply these results to more special cases. Most of these applications combine the "smallness" of the boundaries o...

Variations on Countable Tightness

We consider 9 natural tightness conditions for topological spaces that are all variations on countable tightnes and investigate the interrelationships between them. Several natural open problems are raised.

Pseudocompact Spaces

Pfa(s) and Countable Tightness

Todorcevic introduced the forcing axiom PFA(S) and established many consequences. We contribute to this project. In particular, we consider status under PFA(S) of two important consequences of PFA concerning spaces of countable tightness. In particular we prove that the existence of a Souslin tree does not imply the existence of a compact non-sequential space of countable tightness. We contrast...