Variations on countable tightness
نویسندگان
چکیده
منابع مشابه
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.
متن کاملOn 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.
متن کاملPfa(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...
متن کاملCountable Tightness, Elementary Submodels and Homogeneity
We show (in ZFC) that the cardinality of a compact homogeneous space of countable tightness is no more than 20 .
متن کاملProducts 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Mathematica Hungarica
سال: 2017
ISSN: 0236-5294,1588-2632
DOI: 10.1007/s10474-017-0714-6