A NOTE ON SPACES WHICH HAVE COUNTABLE TIGHTNESS
نویسندگان
چکیده
منابع مشابه
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.
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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...
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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...
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ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2011
ISSN: 1225-1763
DOI: 10.4134/ckms.2011.26.2.297